NODIA AND COMPANY. GATE SOLVED PAPER Mechanical Engineering Thermodynamics. Copyright By NODIA & COMPANY

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1 No art of this ublication may be reroduced or distributed in any form or any means, electronic, mechanical, hotocoying, or otherwise without the rior ermission of the author. GAE SOLVED PAPER Mechanical Engineering hermodynamics Coyright By NODIA & COMPANY Information contained in this book has been obtained by authors, from sources believes to be reliable. However, neither Nodia nor its authors guarantee the accuracy or comleteness of any information herein, and Nodia nor its authors shall be resonsible for any error, omissions, or damages arising out of use of this information. his book is ublished with the understanding that Nodia and its authors are sulying information but are not attemting to render engineering or other rofessional services. NODIA AND COMPANY B8, Dhanshree ower Ist, Central Sine, Vidyadhar Nagar, Jaiur 009 Ph : enquiry@nodia.co.in

2 YEAR 0 ONE MARK Q. A cylinder contains 5m of an ideal gas at a ressure of bar. his gas is comressed in a reversible isothermal rocess till its ressure increases to 5 bar. he work in kj required for this rocess is (A) (B) 95. (C) 98.7 (D) 0. YEAR 0 WO MARKS Q. Secific enthaly and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below: Secific Enthaly ^kj/ kgh Velocity ^m/ sh Inlet steam condition Exit steam condition 60 5 he rate of heat loss from the turbine er kg of steam flow rate is 5kW. Neglecting changes in otential energy of steam, the ower develoed in kw by the steam turbine er kg of steam flow rate is (A) 90. (B) 9. (C) (D) Q. he ressure, temerature and velocity of air flowing in a ie are 5bar, 500 K and 50 m/ s, resectively. he secific heats of air at constant ressure and at constant volume are.005 kj/ kg K and 0.78 kj/ kg K, resectively. Neglect otential energy. If the ressure and temerature of the surrounding are bar and 00 K, resectively, the available energy in kj/ kg of the air stream is (A) 70 (B) 87 (C) 9 (D) Common Data For Q. 4 and 5 In a simle Brayton cycle, the ressure ratio is 8 and temeratures at the entrance of comressor and turbine are 00 K and 400 K, resectively. Both comressor and gas turbine have isentroic efficiencies equal to 08.. For the gas, assume a constant value of c (secific heat at constant ressure) equal to kj/ kg K and ratio of secific heats as. 4. Neglect changes in kinetic and otential energies. Q. 4 he ower required by the comressor in kw/ kg of gas flow rate is (A) 94.7 (B) 4.4 (C) 04. (D) 78.5

3 Q. 5 he thermal efficiency of the cycle in ercentage (%) is (A) 4.8 (B) 8.6 (C) 44.8 (D) 5. YEAR 0 ONE MARK Q. 6 Steam enters an adiabatic turbine oerating at steady state with an enthaly of 5.0 kj/ kg and leaves as a saturated mixture at 5 kpa with quality (dryness fraction) 0.9. he enthalies of the saturated liquid and vaour at 5 kpa are h f 5.94 kj/ kg and h g 598. kj/ kg resectively. he mass flow rate of steam is 0 kg/ s. Kinetic and otential energy changes are negligible. he ower outut of the turbine in MW is (A) 6.5 (B) 8.9 (C) 9. (D) 7.0 Q. 7 A ideal gas of mass m and temerature undergoes a reversible isothermal rocess from an initial ressure to final ressure. he heat loss during the rocess is Q. he entroy change D s of the gas is (A) mr lnb l (B) mr lnb l Q (C) mr lnb l (D) zero YEAR 0 WO MARKS Common Data For Q. 8 and 9 Air enters an adiabatic nozzle at 00 kpa, 500 K with a velocity of 0 m/ s. It leaves the nozzle at 00 kpa with a velocity of 80 m/ s. he inlet area is 80 cm. he secific heat of air c is 008 JkgK /. Q. 8 he exit temerature of the air is (A) 56 K (C) 484 K (B) 5 K (D) 468 K Q. 9 he exit area of the nozzle in cm is (A) 90. (B) 56. (C) 4.4 (D).9 YEAR 0 Q. 0 Heat and work are (A) intensive roerties (B) extensive roerties (B) oint functions (D) ath functions ONE MARK

4 Q. he contents of a wellinsulated tank are heated by a resistor of W in which 0 A current is flowing. Consider the tank along with its contents as a thermodynamic system. he work done by the system and the heat transfer to the system are ositive. he rates of heat (Q), work (W) and change in internal energy ( D U) during the rocess in kw are (A) Q 0, W., DU +. (B) Q +., W 0, DU+. (C) Q., W 0, DU. (D) Q 0, W +., DU. YEAR 0 WO MARKS Q. he values of enthaly of steam at the inlet and outlet of a steam turbine in a Rankine cycle are 800 kj/ kg and 800 kj/ kg resectively. Neglecting um work, the secific steam consumtion in kg/ kw hour is (A).60 (B) 0.6 (C) 0.06 (D) 0.0 Q. he crank radius of a singlecylinder I.C. engine is 60 mm and the diameter of the cylinder is 80 mm. he swet volume of the cylinder in cm is (A) 48 (B) 96 (C) 0 (D) 60 Q. 4 An ideal Brayton cycle, oerating between the ressure limits of bar and 6 bar, has minimum and maximum temerature of 00 K and 500 K. he ratio of secific heats of the working fluid is.4. he aroximate final temeratures in Kelvin at the end of comression and exansion rocesses are resectively (A) 500 and 900 (B) 900 and 500 (C) 500 and 500 (D) 900 and 900 Common Data For Q. 5 and 6 In an exerimental set u, air flows between two stations P and Q adiabatically. he direction of flow deends on the ressure and temerature conditions maintained at P and Q. he conditions at station P are 50 kpa and 50 K. he temerature at station Q is 00 K. he following are the roerties and relations ertaining to air : Secific heat at constant ressure, c.005 kj/ kgk; Secific heat at constant volume, c v 0.78 kj/ kgk; Characteristic gas constant, R 0.87 kj/ kgk Enthaly, h c Internal energy, u c v Q. 5 If the air has to flow from station P to station Q, the maximum ossible value of ressure in kpa at station Q is close to (A) 50 (B) 87 (C) 8 (D) 50

5 Q. 6 If the ressure at station Q is 50 kpa, the change in entroy ( sq sp) in kj/ kgk is (A) (B) 0 (C) 0.60 (D) 0.55 Common Data For Q. 7 and 8 he temerature and ressure of air in a large reservoir are 400 K and bar resectively. A converging diverging nozzle of exit area m is fitted to the wall of the reservoir as shown in the figure. he static ressure of air at the exit section for isentroic flow through the nozzle is 50 kpa. he characteristic gas constant and the ratio of secific heats of air are 0.87 kj/ kgk and.4 resectively. Q. 7 he density of air in kg/ m at the nozzle exit is (A) (B) (C) 0.77 (D) Q. 8 he mass flow rate of air through the nozzle in kg/s is (A).0 (B).77 (C).85 (D).06 YEAR 00 ONE MARK Q. 9 A turbocharged fourstroke direct injection diesel engine has a dislacement volume of m (5.9 litres). he engine has an outut of 950 kw at 00 rm. he mean effective ressure (in MPa) is closest to (A) (B) (C) 0. (D) 0. Q. 0 One kilogram of water at room temerature is brought into contact with a high temerature thermal reservoir. he entroy change of the universe is (A) equal to entroy change of the reservoir (B) equal to entroy change of water (C) equal to zero (D) always ositive

6 YEAR 00 WO MARKS Q. A monoatomic ideal gas ( g.67, molecular weight 40) is comressed adiabatically from 0. MPa, 00 K to 0. MPa. he universal gas constant is 8.4 kjkg mol K. he work of comression of the gas (in kjkg ) is (A) 9.7 (B) 9.9 (C). (D) 0 Q. Consider the following two rocesses ; (a) A heat source at 00 K loses 500 kj of heat to a sink at 800 K (b) A heat source at 800 K loses 000 kj of heat to a sink at 500 K Which of the following statements is true? (A) Process I is more irreversible than Process II (B) Process II is more irreversible than Process I (C) Irreversibility associated in both the rocesses are equal (D) Both the rocesses are reversible Common Data For Q. and 4 In a steam ower lant oerating on the Rankine cycle, steam enters the turbine at 4MPa, 50c C and exists at a ressure of 5 kpa. hen it enters the condenser and exits as saturated water. Next, a um feeds back the water to the boiler. he adiabatic efficiency of the turbine is 90%. he thermodynamic states of water and steam are given in table. State h( kjkg ) s( kjkg K ) ( mkg n ) Steam : 4 MPa, 50cC Water : 5 kpa h f h g s f s g n f h is secific enthaly, s is secific entroy and n the secific volume; subscrits f and g denote saturated liquid state and saturated vaor state. Q. he net work outut ( kjkg ) of the cycle is (A) 498 (B) 775 (C) 860 (D) 957 ng Q. 4 Heat sulied ( kjkg ) to the cycle is (A) 7 (B) 576 (C) 86 (D) 09 YEAR 009 ONE MARK Q. 5 If a closed system is undergoing an irreversible rocess, the entroy of the system (A) must increase (B) always remains constant (C) Must decrease (D) can increase, decrease or remain constant

7 Q. 6 A frictionless istoncylinder device contains a gas initially at 0.8 MPa and 0.05 m. It exands quasistatically at constant temerature to a final volume of 0.00 m. he work outut (in kj) during this rocess will be (A) 8. (B).00 (C) (D) YEAR 009 WO MARKS Q. 7 A comressor undergoes a reversible, steady flow rocess. he gas at inlet and outlet of the comressor is designated as state and state resectively. Potential and kinetic energy changes are to be ignored. he following notations are used : n Secific volume and ressure of the gas. he secific work required to be sulied to the comressor for this gas comression rocess is (A) # dn (B) # nd (C) n ( ) (D) ( n n) Q. 8 In an airstandard Ottocycle, the comression ratio is 0. he condition at the beginning of the comression rocess is 00 kpa and 7c C. Heat added at constant volume is 500 kj/ kg, while 700 kj/ kg of heat is rejected during the other constant volume rocess in the cycle. Secific gas constant for air 0.87 kj/ kgk. he mean effective ressure (in kpa) of the cycle is (A) 0 (B) 0 (C) 55 (D) 0 Q. 9 An irreversible heat engine extracts heat from a high temerature source at a rate of 00 kw and rejects heat to a sink at a rate of 50 kw. he entire work outut of the heat engine is used to drive a reversible heat um oerating between a set of indeendent isothermal heat reservoirs at 7c C and 75c C. he rate (in kw) at which the heat um delivers heat to its high temerature sink is (A) 50 (B) 50 (C) 00 (D) 60 Common Data For Q. 0 and he inlet and the outlet conditions of steam for an adiabatic steam turbine are as indicated in the figure. he notations are as usually followed.

8 Q. 0 If mass rate of steam through the turbine is 0 kg/ s, the ower outut of the turbine (in MW) is (A).57 (B).94 (C) (D) Q. Assume the above turbine to be art of a simle Rankine cycle. he density of water at the inlet to the um is 000 kg/ m. Ignoring kinetic and otential energy effects, the secific work (in kj/ kg) sulied to the um is (A) 0.9 (B) 0.5 (C).90 (D).50 YEAR 008 ONE MARK Q. moles of oxygen are mixed adiabatically with another moles of oxygen in mixing chamber, so that the final total ressure and temerature of the mixture become same as those of the individual constituents at their initial states. he universal gas constant is given as R. he change in entroy due to mixing, er mole of oxygen, is given by (A) R ln (B) 0 (C) R ln (D) R ln 4 Q. Which one of the following is NO a necessary assumtion for the airstandard Otto cycle? (A) All rocesses are both internally as well as externally reversible. (B) Intake and exhaust rocesses are constant volume heat rejection rocesses. (C) he combustion rocess is a constant volume heat addition rocess. (D) he working fluid is an ideal gas with constant secific heats. YEAR 008 WO MARKS Q. 4 A gas exands in a frictionless istoncylinder arrangement. he exansion rocess is very slow, and is resisted by an ambient ressure of 00 kpa. During the exansion rocess, the ressure of the system (gas) remains constant at 00 kpa. he change in volume of the gas is 0.0 m. he maximum amount of work that could be utilized from the above rocess is (A) 0 kj (B) kj (C) kj (D) kj

9 Q. 5 A cyclic device oerates between three reservoirs, as shown in the figure. Heat is transferred to/from the cycle device. It is assumed that heat transfer between each thermal reservoir and the cyclic device takes lace across negligible temerature difference. Interactions between the cyclic device and the resective thermal reservoirs that are shown in the figure are all in the form of heat transfer. he cyclic device can be (A) a reversible heat engine (B) a reversible heat um or a reversible refrigerator (C) an irreversible heat engine (D) an irreversible heat um or an irreversible refrigerator Q. 6 A balloon containing an ideal gas is initially ket in an evacuated and insulated room. he balloon rutures and the gas fills u the entire room. Which one of the following statements is RUE at the end of above rocess? (A) he internal energy of the gas decreases from its initial value, but the enthaly remains constant (B) he internal energy of the gas increases from its initial value, but the enthaly remains constant (C) Both internal energy and enthaly of the gas remain constant (D) Both internal energy and enthaly of the gas increase Q. 7 A rigid, insulated tank is initially evacuated. he tank is connected with a suly line through which air (assumed to be ideal gas with constant secific heats) asses at MPa, 50c C. A valve connected with the suly line is oened and the tank is charged with air until the final ressure inside the tank reaches MPa. he final temerature inside the tank. (A) is greater than 50c C (B) is less than 50cC (C) is equal to 50cC (D) may be greater than, less than, or equal to, 50c C deending on the volume of the tank

10 Q. 8 A thermal ower lant oerates on a regenerative cycle with a single oen feed water heater, as shown in the figure. For the state oints shown, the secific enthalies are: h 800 kj/ kg and h 00 kj/ kg. he bleed to the feed water heater is 0% of the boiler steam generation rate. he secific enthaly at state is (A) 70 kj/kg (C) 500 kj/kg (B) 80 kj/kg (D) 000 kj/kg Q. 9 In a steady state flow rocess taking lace in a device with a single inlet and a single outlet, the work done er unit mass flow rate is given by W # nd, where n is the secific volume and is the ressure. inlet he exression for W given above (A) is valid only if the rocess is both reversible and adiabatic (B) is valid only if the rocess is both reversible and isothermal (C) is valid for any reversible rocess outlet (D) is incorrect; it must be W # dn inlet Common Data For Q. 40 to 4 In the figure shown, the system is a ure substance ket in a istoncylinder arrangement. he system is initially a twohase mixture containing kg of liquid and 0.0 kg of vaour at a ressure of 00 kpa. Initially, the iston rests on a set of stos, as shown in the figure. A ressure of 00 kpa is required to exactly balance the weight of the iston and the outside atmosheric ressure. Heat transfer takes lace into the system until its volume increases by 50%. Heat transfer to the system occurs in such a manner that the iston, when allowed to move, does so in a very slow (quasistatic/quasiequilibrium) rocess. he thermal reservoir from which heat is transferred to the system has a temerature of 400c C. Average temerature of the system boundary can be taken as 75cC. he heat transfer to the system is kj, during which its entroy increases by 0 JK. / outlet

11 Secific volume of liquid ( n f ) and vaour ( n g ) hases, as well as values of saturation temeratures, are given in the table below. Pressure (kpa) Saturation temerature, sat( c C) n (m /kg) f n (m /kg) Q. 40 At the end of the rocess, which one of the following situations will be true? (A) suerheated vaour will be left in the system (B) no vaour will be left in the system (C) a liquid + vaour mixture will be left in the system (D) the mixture will exist at a dry saturated vaour state Q. 4 he work done by the system during the rocess is (A) 0. kj (B) 0. kj (C) 0. kj (D) 0.4 kj g Q. 4 he net entroy generation (considering the system and the thermal reservoir together) during the rocess is closest to (A) 7.5 J/K (B) 7.7 J/K (C) 8.5 J/K (D) 0 J/K YEAR 007 ONE MARK Q. 4 Which of the following relationshis is valid only for reversible rocesses undergone by a closed system of simle comressible substance (neglect changes in kinetic and otential energy?) (A) dq du+ dw (B) ds du + dn (C) ds du + dw (D) dq du+ dn

12 Q. 44 Water has a critical secific volume of m / kg. A closed and rigid steel tank of volume 0.05 m contains a mixture of water and steam at 0. MPa. he mass of the mixture is 0 kg. he tank is now slowly heated. he liquid level inside the tank (A) will rise (B) will fall (C) will remain constant (D) may rise or fall deending on the amount of heat transferred YEAR 007 WO MARKS Q. 45 he stroke and bore of a four stroke sark ignition engine are 50 mm and 00 mmresectively. he clearance volume is 0.00 m. If the secific heat ratio g.4, the airstandard cycle efficiency of the engine is (A) 46.40% (B) 56.0% (C) 58.0% (D) 6.80% Q. 46 Which combination of the following statements is correct? P : A gas cools uon exansion only when its Joulehomson coefficient is ositive in the temerature range of exansion. Q : For a system undergoing a rocess, its entroy remains constant only when the rocess is reversible. R : he work done by closed system in an adiabatic is a oint function. S : A liquid exands uon freezing when the sloe of its fusion curve on ressureemerature diagram is negative. (A) R and S (B) P and Q (C) Q, R and S (D) P, Q and R Q. 47 Which combination of the following statements is correct? he incororation of reheater in a steam ower lant : P : always increases the thermal efficiency of the lant. Q : always increases the dryness fraction of steam at condenser inlet R : always increases the mean temerature of heat addition. S : always increases the secific work outut. (A) P and S (B) Q and S (C) P, R and S (D) P, Q, R and S

13 Common Data For Q. 48 and 49 A thermodynamic cycle with an ideal gas as working fluid is shown below. Q. 48 he above cycle is reresented on s lane by Q. 49 If the secific heats of the working fluid are constant and the value of secific heat ratio is.4, the thermal efficiency (%) of the cycle is (A) (B) 40.9 (C) 4.6 (D) 59.7 Q. 50 A heat transformer is device that transfers a art of the heat, sulied to it at an intermediate temerature, to a high temerature reservoir while rejecting the remaining art to a low temerature heat sink. In such a heat transformer, 00 kj of heat is sulied at 50 K. he maximum amount of heat in kj that can be transferred to 400 K, when the rest is rejected to a heat sink at 00 K is (A).50 (B) 4.9 (C). (D) 57.4

14 YEAR 006 WO MARKS Q. 5 Given below is an extract from steam tables. emerature in cc sat (Bar) Secific volume m /kg Enthaly (kj/ kg) Saturated Liquid Saturated Vaour Saturated Liquid Saturated Vaour Secific enthaly of water in kj/kg at 50 bar and 45c C is (A) 0.60 (B) 00.5 (C) 96.8 (D) Q. 5 Determine the correctness or otherwise Assertion (A) and the Reason (R) Assertion (A) : In a ower lant working on a Rankine cycle, the regenerative feed water heating imroves the efficiency of the steam turbine. Reason (R) : he regenerative feed water heating raises the average temerature of heat addition in the Rankine cycle. (A) Both (A) and (R) are true and (R) is the correct reason for (A) (B) Both (A) and (R) are true but (R) is NO the correct reason for (A) (C) Both (A) and (R) are false (D) (A) is false but (R) is true Q. 5 Determine the correctness or otherwise of the following Assertion (A) and the Reason (R). Assertion (A) : Condenser is an essential equiment in a steam ower lant. Reason (R) : For the same mass flow rate and the same ressure rise, a water um requires substantially less ower than a steam comressor. (A) Both (A) and (R) are true and (R) is the correct reason for (A) (B) Both (A) and (R) are true and (R) is NO the correct reason for (A) (C) Both (A) and (R) are false (D) (A) is false but (R) is true Q. 54 Match items from grous I, II, III, IV and V. Grou I Grou II Grou III Grou IV Grou V When added to the system is Differential Function Phenomenon E Heat G Positive I Exact K Path M ransient F Work H Negative J Inexact L Point N Boundary (A) FGJKM (B) EGIKM EGIKN FHIKN (C) FHJLN (D) EGJKN EHILM FHJKM

15 Q. 55 Grou I shows different heat addition rocess in ower cycles. Likewise, Grou II shows different heat removal rocesses. Grou III lists ower cycles. Match items from Grous I, II and III. Grou I Grou II Grou III P. Pressure constant S. Pressure constant. Rankine Cycle Q. Volume Constant. Volume Constant. Otto cycle R. emerature constant U. emerature Constant. Carnot cycle 4. Diesel cycle 5. Brayton cycle (A) PS5 (B) PS RU RU PS PS4 Q P (C) R (D) P4 PS RS P4 PS QS5 PS5 Common Data For Q. 56 and 57 A football was inflated to a gauge ressure of bar when the ambient temerature was 5c C. When the game started next day, the air temerature at the stadium was 5c C. Assume that the volume of the football remains constant at 500 cm. Q. 56 he amount of heat lost by the air in the football and the gauge ressure of air in the football at the stadium resectively equal (A) 0.6 J,.94 bar (B).8 J, 0.9 bar (C) 6. J,.94 bar (D) 4.7 J, 0.9 bar Q. 57 Gauge ressure of air to which the ball must have been originally inflated so that it would be equal bar gauge at the stadium is (A). bar (B).94 bar (C).07 bar (D).00 bar YEAR 005 ONE MARK Q. 58 he following four figures have been drawn to reresent a fictitious thermodynamic cycle, on the n and s lanes.

16 According to the first law of thermodynamics, equal areas are enclosed by (A) figures and (B) figures and (C) figures and 4 (D) figures and Q. 59 A v diagram has been obtained from a test on a recirocating comressor. Which of the following reresents that diagram? YEAR 005 WO MARKS Q. 60 A reversible thermodynamic cycle containing only three rocesses and roducing work is to be constructed. he constraints are (i) there must be one isothermal rocess, (ii) there must be one isentroic rocess, (iii) the maximum and minimum cycle ressures and the clearance volume are fixed, and (iv) olytroic rocesses are not allowed. hen the number of ossible cycles are (A) (B) (C) (D) 4

17 Q. 6 Nitrogen at an initial state of 0 bar, m and 00 K is exanded isothermally to a final volume of m. he n relation is a R a + n k n, where a > 0. he final ressure. (A) will be slightly less than 5 bar (B) will be slightly more than 5 bar (C) will be exactly 5 bar (D) cannot be ascertained in the absence of the value of a Q. 6 In the velocity diagram shown below, u blade velocity, C absolute fluid velocity and W relative velocity of fluid and the subscrits and refer to inlet and outlet. his diagram is for (A) an imulse turbine (C) a centrifugal comressor (B) a reaction turbine (D) an axial flow comressor Common Data For Q. 6 and 64 In two air standard cyclesone oerating in the Otto and the other on the Brayton cycleair is isentroically comressed from 00 to 450 K. Heat is added to raise the temerature to 600 K in the Otto cycle and to 550 K in the Brayton cycle. Q. 6 In ho and h B are the efficiencies of the Otto and Brayton cycles, then (A) h 0.5, h 0.8 O B (B) h h 0. O B (C) h 0.5, h 0.45 O B (D) it is not ossible to calculate the efficiencies unless the temerature after the exansion is given Q. 64 If WO and WB are work oututs er unit mass, then (A) WO > WB (B) W < W (C) W O O B W B (D) it is not ossible to calculate the work oututs unless the temerature after the exansion is given Common Data For Q. 65 and 66 he following table of roerties was rinted out for saturated liquid and saturated vaour of ammonia. he title for only the first two columns are available. All that we know that the other columns (column to 8) contain data on secific roerties, namely, internal energy (kj/kg), enthaly (kj/kg) and entroy (kj/ kg.k)

18 t( cc) (kpa) Q. 65 he secific enthaly data are in columns (A) and 7 (B) and 8 (C) 5 and 7 (D) 5 and 8 Q. 66 When saturated liquid at 40c C is throttled to 0cC, the quality at exit will be (A) 0.89 (B) 0. (C) 0. (D) YEAR 004 ONE MARK Q. 67 A gas contained in a cylinder is comressed, the work required for comression being 5000 kj. During the rocess, heat interaction of 000 kj causes the surroundings to be heated. he changes in internal energy of the gas during the rocess is (A) 7000 kj (B) 000 kj (C) kj (D) kj Q. 68 he comression ratio of a gas ower lant cycle corresonding to maximum work outut for the given temerature limits of min and max will be (A) max ( g ) b l (B) min ( g b l ) min g (C) max g b l (D) min b l max min g Q. 69 At the time of starting, idling and low seed oeration, the carburretor sulies a mixture which can be termed as (A) Lean (B) slightly leaner than stoichiometric (C) stoichiometric (D) rich max g g g YEAR 004 WO MARKS Q. 70 A steel billet of 000 kg mass is to be cooled from 50 K to 450 K. he heat released during this rocess is to be used as a source of energy. he ambient temerature is 0 K and secific heat of steel is 0.5 kj/ kg K. he available energy of this billet is (A) MJ (B) 0.95 MJ (C) 0.5 MJ (D) 0.0 MJ

19 Q. 7 During a Morse test on a 4 cylinder engine, the following measurements of brake ower were taken at constant seed. All cylinders firing 07 kw Number cylinder not firing 0 kw Number cylinder not firing 0 kw Number cylinder not firing 00 kw Number 4 cylinder not firing 098 kw he mechanical efficiency of the engine is (A) 9.5% (B) 85.07% (C) 8.07% (D) 6.% Q. 7 A solar collector receiving solar radiation at the rate of 0.6 kw/ m transforms it to the internal energy of a fluid at an overall efficiency of 50%. he fluid heated to 50 K is used to run a heat engine which rejects heat at 5 K. If the heat engine is to deliver.5 kw ower, the minimum area of the solar collector required would be (A) 8. m (B) 6.66 m (C) 9.68 m (D) 79.6 m Q. 7 An engine working on air standard Otto cycle has a cylinder diameter of 0 cm and stroke length of 5 cm. he ratio of secific heats for air is.4. If the clearance volume is 96. cc and the heat sulied er kg of air er cycle is 800 kj/ kg, the work outut er cycle er kg of air is (A) 879. kj (B) 890. kj (C) 895. kj (D) 97.5 kj Common Data For Q. 74 and 75 Consider a steam ower lant using a reheat cycle as shown. Steam leaves the boiler and enters the turbine at 4 MPa, 50c C ( h 095 kj/kg). After exansion in the turbine to 400 kpa ( h kj/kg), and then exanded in a low ressure turbine to 0 kpa ( h 6 65 kj/kg). he secific volume of liquid handled by the um can be assumed to be

20 Q. 74 he thermal efficiency of the lant neglecting um work is (A) 5.8% (B) 4.% (C) 48.5% (D) 58.6% Q. 75 he enthaly at the um discharge ( h ) is (A) 0. kj/kg (B). kj/kg (C) 4.0 kj/k (D). kj/kg YEAR 00 ONE MARK Q. 76 For a sark ignition engine, the equivalence ratio ( f ) of mixture entering the combustion chamber has values (A) f < for idling and f > for eak ower conditions (B) f > for both idling and eak ower conditions (C) f > for idling and f < for eak ower conditions (D) f < for both idling and eak ower conditions Q. 77 A diesel engine is usually more efficient than a sark ignition engine because (A) diesel being a heavier hydrocarbon, releases more heat er kg than gasoline (B) the air standard efficiency of diesel cycle is higher than the Otto cycle, at a fixed comression ratio (C) the comression ratio of a diesel engine is higher than that of an SI engine (D) self ignition temerature of diesel is higher than that of gasoline Q. 78 In Ranking cycle, regeneration results in higher efficiency because (A) ressure inside the boiler increases (B) heat is added before steam enters the low ressure turbine (C) average temerature of heat addition in the boiler increases (D) total work delivered by the turbine increases Q. 79 Considering the variation of static ressure and absolute velocity in an imulse steam turbine, across one row of moving blades (A) both ressure and velocity decreases (B) ressure decreases but velocity increases (C) ressure remains constant, while velocity increases (D) ressure remains constant, while velocity decreases Q. 80 A kw, 40 liters water heater is switched on for 0 minutes. he heat caacity c for water is 4. kj/ kgk. Assuming all the electrical energy has gone into heating the water, increase of the water temerature in degree centigrade is (A).7 (B) 4.0 (C) 4. (D) 5.5

21 YEAR 00 WO MARKS Q. 8 Considering the relationshi ds du + dn between the entroy ( s ), internal energy ( U ), ressure ( ), temerature ( ) and volume ( n ), which of the following statements is correct? (A) It is alicable only for a reversible rocess (B) For an irreversible rocess, ds > du + dn (C) It is valid only for an ideal gas (D) It is equivalent to I st law, for a reversible rocess Q. 8 In a gas turbine, hot combustion roducts with the secific heats c 0.98 kj/ kgk, and c v kj/ kgk enters the turbine at 0 bar, 500 K exit at bar. he isentroic efficiency of the turbine is he work develoed by the turbine er kg of gas flow is (A) kj/kg (B) kj/kg (C) kj/kg (D).00 kj/kg Q. 8 An automobile engine oerates at a fuel air ratio of 0.05, volumetric efficiency of 90 % and indicated thermal efficiency of 0 %. Given that the calorific value of the fuel is 45 MJ/ kg and the density of air at intake is kg/ m, the indicated mean effective ressure for the engine is (A) bar (B) 6.75 bar (C) 67.5 bar (D) 4 bar Q. 84 For an engine oerating on air standard Otto cycle, the clearance volume is 0 % of the swet volume. he secific heat ratio of air is.4. he air standard cycle efficiency is (A) 8. % (B) 9. 8% (C) 60. % (D) 6. 7% Common Data For Q. 85 and 86 Nitrogen gas (molecular weight 8) is enclosed in a cylinder by a iston, at the initial condition of bar, 98 K and m. In a articular rocess, the gas slowly exands under isothermal condition, until the volume becomes m. Heat exchange occurs with the atmoshere at 98 K during this rocess. Q. 85 he work interaction for the Nitrogen gas is (A) 00 kj (B) 8.6 kj (C) kj (D) 00 kj Q. 86 he entroy changes for the Universe during the rocess in kj/k is (A) (B) (C) 0 (D) 0.67

22 YEAR 00 Q. 87 A ositive value of Joulehomson coefficient of a fluid means (A) temerature dros during throttling (B) temerature remains constant during throttling (C) temerature rises during throttling (D) None of the above ONE MARK Q. 88 A correctly designed convergentdivergent nozzle working at a designed load is (A) always isentroic (B) always choked (C) never choked (D) never isentroic YEAR 00 WO MARKS Q. 89 A Carnot cycle is having an efficiency of If the temerature of the high temerature reservoir is 77c C, what is the temerature of low temerature reservoir? (A) c C (B) cc (C) 0c C (D) 50cC Q. 90 An ideal air standard Otto cycle has a comression ratio of 8.5. If the ratio of the secific heats of air ( g ) is.4, what is the thermal efficiency in ercentage) of the Otto cycle? (A) (B) (C) 5. 5 (D) 95 Q. 9 he efficiency of suerheat Rankine cycle is higher than that of simle Rankine cycle because (A) the enthaly of main steam is higher for suerheat cycle (B) the mean temerature of heat addition is higher for suerheat cycle (C) the temerature of steam in the condenser is high (D) the quality of steam in the condenser is low. YEAR 00 Q. 9 he Rateau turbine belongs to the category of (A) ressure comounded turbine (B) reaction turbine (C) velocity comounded turbine (D) radial flow turbine ONE MARK Q. 9 A gas having a negative Joulehomson coefficient ( m < 0), when throttled, will (A) become cooler (B) become warmer (C) remain at the same temerature (D) either be cooler or warmer deending on the tye of gas

23 YEAR 00 WO MARKS Q. 94 A cyclic heat engine does 50 kj of work er cycle. If the efficiency of the heat engine is 75 %, the heat rejected er cycle is (A) 6 kj (B) kj (C) 7 kj (D) 66 kj Q. 95 A singleacting twostage comressor with comlete intercooling delivers air at 6 bar. Assuming an intake state of bar at 5c C, the ressure ratio er stage is (A) 6 (B) 8 (C) 4 (D) Q. 96 A small steam whistle (erfectly insulated and doing no shaft work) causes a dro of 0.8 kj/ kg in the enthaly of steam from entry to exit. If the kinetic energy of the steam at entry is negligible, the velocity of the steam at exit is (A) 4 m/ s (B) 40 m/ s (C) 80 m/ s (D) 0 m/ s Q. 97 In a sark ignition engine working on the ideal Otto cycle, the comression ratio is 55.. he work outut er cycle (i.e., area of the n diagram) is equal to 5.65 # 0 # nc, where n c is the clearance volume in m. he indicated mean effective ressure is (A) bar (B) 5.50 bar (C) bar ******** (D) bar

24 SOLUION Sol. Otion (A) is correct. For Reversible isothermal Process work done is given by W v ln ln # # # b 5 l Sol. Sol kj he negative sign shows that the comression rocess is taking lace in this rocess. Otion (A) is correct. From energy balance equation for steady flow system E in E out h V + + gz + dq h V + + gz + dw For negligible P.E. gz gz 0 or dw h h V V + ^ h + dq # 000 8^80h ^5hB ^50 60h + 5 # kw/ kg Otion (B) is correct. IN ie 5bar 5# 0 5 Pa, 500 K, V 50 m/ sec c.005 kj/ kg K, cv 0.78 kj/ kg K For surrounding air 0 bar # 0 5 Pa, 0 00 K Available energy function is y h h S S V ^ 0h 0^ 0h+ + gz Given, the otential energy is negligible. hus y h h S S V ^ 0h 0^ 0h+ he entroy is given by S c ln Rln and h c So that y c c ln Rln c ln Rln V ^ 0h 0: D y c c ln ln R V ^ 0h 0; c m b + le 0 0

25 Sol ln ln 00 5 ^50h ^ h ; # b l # b le+ # kj/ kg Otion (C) is correct. he v and s diagram of brayton cycle is shown below: Given r 8, g.4, 00 K, 400 K, c kj/ kgk, h isen 0.8 he rocess (Isentroic comression) Process l (Actual comression) Process 4 (Isentroic exansion) Process 4l (Actual exansion) For reversible adiabatic comression rocess g b 8 l ^ h g or 00 # ^8h K Now Isentroic comressor work h isen Actual comressor work mc o ( ) W actual hisen 7 Sol. 5 # ^ h o 0.8 Wnet m Otion (A) is correct. For rocess ( constant) V V 04. kw/ kg Heat sulied Q in c ^ lh Now h W isen W actual isen or l h hl h c ^ h c ^l h l l 00

26 Sol. 6 Sol. 7 l 604. K So that Q in # ^ h kj/ kg For rocess 4 ( constant) g g g c 4 m ^r h g 4 or g K ^rh g ^8h 4. Now h isen 08. or 4 l K Wactual h h4 4 l l Wisen h h l Now W act c ^4l h ^ h 50.7 kj/ kg Hence Wact Wcom n thermal Qin b l# % Otion (B) is correct. For adiabatic exansion steam in turbine. Given h 5.0 kj/ kg, m 0 kg/ s, x 0.9 ( dryness fraction) At 5 kpa Enthaly of liquid, h f 5.94 kj/ kg Enthaly of vaour, h g 598. kj/ kg Since Power outut of turbine. P mh o ( h) ( K. E and P. E are negligible ) h h + xh h + x( h h ) From Eq. (i) f fg f g f ( ) kj/ kg P 0 # ( ) 8899 kw 8.9 MW...(i) Otion (B) is correct. We know that ds du + Pdn...(i) For ideal gas n mr For isothermal rocess constant

27 Sol. 8 Sol. 9 Sol. 0 For reversible rocess du 0 hen from equation (i) d ds n mr d mr n n d n n n # ds Ds mr d # mr ln n n n n D s n mr ln Otion (C) is correct. From energy balance for steady flow system. E in E out As h c Equation () becomes c V + c V + n : D n mh V ob + l mh V ob + l...(i) V V c + # c m K # 008 Otion (D) is correct. From Mass conservation. mo in mo out VA VA...(i) n n where n secific volume of air R herefore Eq. () becomes VA VA R R V A A # # # 00 # 0 # 80 # cm # V# 00 # 80 # 500 Otion (D) is correct. Work done is a quasistatic rocess between two given states deends on the ath followed. herefore, # dw! W W dw shows the inexact differential But, # dw W or W So, Work is a ath function and Heat transfer is also a ath function. he amount of heat transferred when a system changes from state to state deends on the intermediate states through which the system asses i.e. the ath. # dq Q or Q dq shows the inexact differential. So, Heat and work are ath functions.

28 Sol. Sol. Sol. Sol. 4 Otion (A) is correct. Given : R W, i 0 A Since work is done on the system. So, W electrical i R (0) # 00 W. kw Here given that tank is wellinsulated. So, D Q 0 Alying the First law of thermodynamics, D Q DU+ DW DU+ DW 0 D W DU And D U +. kw Heat is transferred to the system Otion (A) is correct. Given : h 800 kj/ kg Enthaly at the inlet of steam turbine h 800 kj/ kg Enthaly at the outlet of a steam turbine Steam rate or secific steam consumtion 600 kg/ kwh W W Pum work W is negligible, therefore Steam rate 600 kg/ kwh W And W h h From Rankine cycle Steam rate 600 kg/ kwh kg/ kwh h h Otion (D) is correct. Given : r 60 mm, D 80 mm Stroke length, L r # 60 0 mm (cylinder diameter) Swet Volume, n s A# L D L 4 # (8.0). 0 4 # ( ) 4 8 # 8 # cm Otion (A) is correct. Given n curve shows the Brayton Cycle. Given : bar 4, 6bar, minimum 00 K, maximum 500 K

29 Sol. 5 Sol. 6 c c v g 4. We have to find (temerature at the end of comression) or 4 (temerature at the end of exansion) Alying adiabatic equation for rocess, we get g 4. g 4. b l b 6 l b 6 l minimum K 500 K ^6 h Again alying for the Process 4, 4 4 g b l b l g g g b 6 l b6 l 086. So, 4 # b6 l 500 # b6 l 900 K maximum Otion (B) is correct. Given : At station : 50 kpa, 50 K At station Q :?, 00 K We know, c g cv Alying adiabatic equation for station P and Q, b l g g g g b l 50 g g 50. b l b 00 l Otion (C) is correct. Given : kpa 87 kpa. 7 Pressure at Q 50 kpa Using the general relation to find the entroy changes between P and Q ds dh nd ds dh n d...(i) Given in the revious art of the question h c Differentiating both the sides, we get dh cd Put the value of dh in equation (i), ds c d n d From the gas equation n / R/ So, c d d R Integrating both the sides and utting the limits Q Q Q # ds c d d # R # P P P

30 Sol. 7 Otion (C) is correct. s Q c R P@ Q Q 6@ s P ln P 6 sp c6ln Qln P@ R6ln Qln P@ Q Q c lnc R ln m b P l P.005 ln ln 50 b 50 l b50 l. 005 #(0. 54) #(. 099) 0.60 kj/ kg K Q P Sol. 8 Given : 400 K, bar, A m, 50 kpa 0.5 bar, c R 0.87 kj/ kg K, g.4,? c v Alying adiabatic equation for isentroic (reversible adiabatic) flow at section () and (), we get g g b l b l g g.4 b l b l. 400 # (. 0 66) K Aly erfect Gas equation at the exit, n mr m R r R n r 50 # 0 R 0.77 kg/ m # 0 # 9. 7 Otion (D) is correct. Given : r 0.77 kg/ m, A m, V? For isentroic exansion, V c ( ) m a n rk #. 005 # 0 #( ) for air c.005 kj/ kg K m/ sec Mass flow rate at exit, mo r AV # # kg/ sec

31 Sol. 9 Otion (A) is correct. Given : n m, Work outut 950 kw, N 00 rm Mean effective ressure me Net work for one cycle 60 dislacement volume # Number of ower cycle n N ( for 4 stroke) Sol. 0 Sol. Sol. Hence, net work for one cycle 950 # W 00 So, me 60 # Pa MPa # Otion (D) is correct. We know that, Entroy of universe is always increases. D s universe > 0 ( Ds) system + ( Ds) surrounding > 0 Otion (A) is correct. 6 5 Given : g.67, M 40, 0. MPa 0 # 0. 0 Pa 5 00 K, 0. MPa # 0 Pa, R u 8.4 kj/ kgmol K Gas constant Universal Gas constant Molecular Weight R Ru kj/ kg K M 40 For adiabatic rocess, g g b l b () 0. l 00 # () #. 96 K Work done in adiabatic rocess is given by, n n R ( ) W g g [ 00 96] ( 96) kj/ kg ( Negative sign shows the comression work) Otion (B) is correct. We know from the clausius Inequality, dq If # 0, the cycle is reversible dq # < 0, the cycle is irreversible and ossible For case (a), For case (b), dq a# kj/ kg

32 Sol. dq dq b# a# > b# dq So, rocess (b) is more irreversible than rocess (a) Otion (C) is correct. Given s curve is for the steam lant.5 kj/ kg 6 Given : 4MPa 4# 0 Pa, 50 cc (7 + 50) K 6 K 5 kpa 5 # 0 Pa, h adiabatic 90% 0.9 Now from the steam table, Given data : h 09.5 kj/ kg, h h f 5.94 kj/ kg, h g 599. kj/ kg Where, From the table, we have s s s + x( s s )...(i) f g f From equation (i), x x dryness fraction s f kj/ kg K s g kj/ kg K s 6.58 s s s s s g f f h h + x( h h ) ( ) f g f kj/ kg heoretical turbine work from the cycle is given by, W h h kj/ kg Actual work by the turbine, heoretical work #hadiabatic Pum work, W ( ) 0. 9 # kj/ kg n f ( ) 4.04 kj/ kg W net W W kj/ kg. 860

33 Sol. 4 Otion (C) is correct. Heat sulied h h4 From s diagram From the um work equation, W h4h h 4 W + h kj/ kg And Heat sulied, Q h h kj/ kg Sol. 5 Otion (A) is correct. We consider the cycle shown in figure, where A and B are reversible rocesses and C is an irreversible rocess. For the reversible cycle consisting of A and B. dq dq dq + 0 A B or dq dq # A # B...(i) For the irreversible cycle consisting of A and C, by the inequality of clausius, dq dq dq # < 0 # A +# C...(ii) From equation (i) and (ii) dq dq # B +# < 0 C dq dq # > B # C...(iii) Since the ath B is reversible, dq # ds B # B Since entroy is a roerty, entroy changes for the aths B and C would be the same. herefore, # ds # ds...(iv) R# # # B From equation (iii) and (iv), C hus, for any irreversible rocess, # C # dq ds > C dq ds > So, entroy must increase. Sol. 6 Otion (A) is correct. Given : 0.8 MPa, n 0.05 m, n 0.00 m, Constant We know work done in a constant temerature (isothermal) rocess W n ln n 6 an k (0.8 0 )(0.05) ln # b l 8. kj

34 Sol. 7 Otion (B) is correct. Sol. 8 Steady flow energy equation for a comressor (Fig a) gives, h + dq h + dw x...(i) Neglecting the changes of otential and kinetic energy. From the roerty relation ds dh nd For a reversible rocess, ds dq So, dq dh nd...(ii) If consider the rocess is reversible adiabatic then dq 0 From equation (i) and (ii), h h dw x & dh h h dw x...(iii) And dh nd...(iv) From equation (iii) and (iv), dw x nd W x # nd Negative sign shows the work is done on the system (comression work) for initial and Final Stage W x # n d Otion (D) is correct. Given : r 0, 00 kpa, 7 cc (7 + 7) K 00 K Q s 500 kj/ kg, Q r 700 kj/ kg, R 0.87 kj/ kg K Mean Effective ressure Net work outut m Swet Volume...(i) Swet volume, n n n ( r ) where n otal volume and n Clearance volume r 0 n n & n 0v...(ii) Alying gas equation for the beginning rocess, n R n R m / kg # 00 From equation (i) n n m / kg 0 0 W net Qs Qr ( ) kj/ kg K 800 kj/ kg K m n ( r ) ( 0 ) kpa b 0 kpa

35 Sol. 9 Otion (C) is correct. Sol. 0 he coefficient of erformance of a Heat um for the given system is, Q Q ( COP ) HP.. Q Q4 W For a reversible rocess, Q Q4 4 ( COP ) Q HP.. 4 W 48 Q Q 48 # K 58 Otion (A) is correct. Given : h 00 kj/ kg, V 60 m/ sec, z 0 m ma, mo dm 0 kg/ sec dt It is a adiabatic rocess, So dq 0 Aly steady flow energy equation [ SFEE....] at the inlet and outlet section of steam turbine, h V dq + + zg + h V zg dw dm dm dq So 0 dm dq 0 And h V + + zg h V zg dw dm dw ( h h ) V V + ( z z ) g dm b l+ ( 60) ( 00) (00 600) # 0 + ; (0 6)9.8 E dw Jkg / kj/ kg dm Power outut of turbine P Mass flow rate dw # dm 0 # # 0 m o 0 kg/ sec P.57 MJ/ sec.57 MW

36 Sol. Otion (C) is correct. Given : r 000 kg/ m Here given that ignoring kinetic and otential energy effects, So in the steady flow energy equation the terms V /, Z g are equal to zero and dq is also zero for adiabatic rocess. S.F.E.E. is reduces to, dw h 4 h + Here, W dm reresents the um work where h Enthaly at the inlet of um and h 4 Enthaly at the outlet of the um. Sol. Sol. dw h 4 h dh...(i) dm For reversible adiabatic comression, dq dh nd ( dq 0) dh nd...(ii) From equation (i) and (ii), we get dw nd ( ) v dm r r dw (000 70)kPa 9 kpa dm kpa Otion (B) is correct. Given :, Universal Gas constant R. Here given oxygen are mixed adiabatically So, dq 0 dq We know, ds 0 0 Otion (B) is correct. Sol. 4 Assumtions of air standard otto cycle : (A) All rocesses are both internally as well as externally reversible. (B) Air behaves as ideal gas (C) Secific heats remains constant ( c & c ) (D) Intake rocess is constant volume heat addition rocess and exhaust rocess is constant volume heat rejection rocess. Intake rocess is a constant volume heat addition rocess, From the given otions, otion () is incorrect. Otion (C) is correct. Given : a 00 kpa, s 00 kpa, D n 0.0 m Net ressure work on the system, v

37 00 00 s a 00 kpa Sol. 5 Sol. 6 For constant ressure rocess work done is given by W Dn 00 # 0. 0 kj Otion (A) is correct. A heat engine cycle is a thermodynamic cycle in which there is a net Heat transfer from higher temerature to a lower temerature device. So it is a Heat Engine. Alying Clausius theorem on the system for checking the reversibility of the cyclic device. dq 0 R# Q Q Q # # 0 60 # Here, the cyclic integral of dq/ is zero. his imlies, it is a reversible Heat engine. Otion (C) is correct. We know enthaly, h U+ n...(i) Where, U Internal energy Pressure of the room n Volume of the room It is given that room is insulated, So there is no interaction of energy (Heat) between system (room) and surrounding (atmoshere). It means Change in internal Energy du 0 and U Constant And temerature is also remains constant. Alying the erfect gas equation, n nr n Constant herefore, from equation (i) h Constant So this rocess is a constant internal energy and constant enthaly rocess. Alternate Method : We know that enthaly, h U+ n Given that room is insulated, So there is no interaction of Energy (Heat) between system (room) and surrounding (atmoshere).

38 Sol. 7 Sol. 8 Sol. 9 It means internal Energy du 0 and U constant. Now flow work n must also remain constant thus we may conclude that during free exansion rocess n i.e. roduct of ressure and secific volume change in such a way that their roduct remains constant. So, it is a constant internal energy and constant enthaly rocess. Otion (A) is correct. Given : MPa, 50 cc (50 + 7) K 6 K For air g.4 We know that final temerature ( ) inside the tank is given by, g. 4 # K 599.cC is greater than 50c C. Otion (A) is correct. Given : h 800 kj/ kg, h 00 kj/ kg From the given diagram of thermal ower lant, oint is directed by the Boiler to the oen feed water heater and oint is directed by the um to the oen feed water Heater. he bleed to the feed water heater is 0% of the boiler steam generation i.e. 0% of h So, h 0% of h + 80% of h Otion (C) is correct. From the first law of thermodynamic, dq du + dw 0. # # kj/ kg dw dq du...(i) If the rocess is comlete at the constant ressure and no work is done other than the dn work. So dq du + dn At constant ressure dn dn ( ) ( dq ) du + d( n) du ( + n) ( dh) h U+ n From equation (i) dw dh + dq dh + ds ds dq/...(ii) For an reversible rocess, ds dh nd nd dh + ds...(iii) From equation (ii) and (iii) dw nd On integrating both sides, we get W # nd It is valid for reversible rocess.

39 Sol. 40 Sol. 4 Sol. 4 Otion (A) is correct. When the vaour is at a temerature greater than the saturation temerature, it is said to exist as suer heated vaour. he ressure and emerature of suerheated vaour are indeendent roerties, since the temerature may increase while the ressure remains constant. Here vaour is at 400c C and saturation temerature is 00c C. So, at 00 kpa ressure suerheated vaour will be left in the system. Otion (D) is correct. Given : 00 kpa, 00 kpa. Let, n n Now, given that Heat transfer takes lace into the system until its volume increases by 50% So, n n+ 50% of n Now, for work done by the system, we must take ressure is 00 kpa, because work done by the system is against the ressure and it is a ositive work done. From first law of thermodynamics, dq du + dw...(i) But for a quasistatic rocess, Constant herefore, change in internal energy is du 0 From equation (i) dq dw dn dw dn [ n n ] For initial condition at 00 kpa,volume n m m liquid # + vaour r # r Here r f nf 0. 00, ng 0. r m liquid g kg, m vaour 0.0 kg So n # # 0. 4# 0 m n m n # # # f g 00 0 n # : n D 00 #[ 6 # 0 4 # 0 ] 00 # # kj Otion (C) is correct. D s net ( Ds) system + ( Ds) surrounding...(i) And it is given that, ( D s) system 0 kj Q Also, ( D s) surrounding b l surrounding Heat transferred to the system by thermal reservoir, 400cC ( ) K 67 K Q kj ( D s) surrounding JK / 67

40 Sol. 4 From equation (i) ( D s) net JK / (ake Negative sign, because the entroy of surrounding decrease due to heat transfer to the system.) Otion (D) is correct. In this question we discuss on all the four otions. (A) dq du+ dw his equation holds good for any rocess undergone by a closed stationary system. (B) ds du + dn his equation holds good for any rocess reversible or irreversible, undergone by a closed system. (C) ds du + dw his equation holds good for any rocess, reversible or irreversible, and for any system. (D) dq du+ dn his equation holds good for a closed system when only dn work is resent. his is true only for a reversible (quasistatic) rocess. Sol. 44 Sol. 45 Otion (A) is correct. Given : n cri m / kg, n 0.05 m, 0. MPa and m 0 kg We know, Rigid means volume is constant. Secific volume, n S m n m / kg 0 05 We see that the critical secific volume is more than the secific volume and during the heating rocess, both the temerature and the ressure remain constant, but the secific volume increases to the critical volume (i.e. critical oint). he critical oint is defined as the oint at which the saturated liquid and saturated vaour states are identical. So, oint (B) will touch the saturated liquid line and the liquid line will rise at the oint O. Otion (C) is correct. Given : L 50 mm 0.5 m, D 00 mm 0. m, n c 0.00 m c, g.4 c Swet volume Comression ratio v n s A# L ( D) L 4 # (.) # m c s r n n n n n Air standard efficiency h () r (. 885) c c g 4.