HEAT- I Part - A C D A B. Te m p. Heat input

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1 e m p HE- I Part -. solid material is supplied with heat at a constant rate. he temperature of the material is changing with heat input as shown in the graph. Study the graph carefully and answer the following questions ; (a) What do the horizontal regions and represent? (b) if =, what do you infer? (c) What does the slope E represent? (d) he slope of O > slope of. What does this indicate? O E Heat input. steel scale is to be prepared such that the millimeter intervals are to be accurate within mm at a certain temperature. etermine the maximum permissible variation during the ruling of the millimeter marks α = / 0 3. vaccum pump is connected to an insulating flask, containing 50 gm of water at 0 o. s the water vapour is being pumped out, some water evaporates and some water solidifies. If the latent of water of vapourisation at 0 o is. 0 6 J/kg and the latent heat of solidification of water is J/kg.calculate the maximum mass of ice that can be formed by this process. 4. he capacity of air conditioners is sometimes expressed in Watts or tons, the latter being the number of tons of ice that can be frozen from water at 0 o in 4 hrs by the unit. Express the capacity of oneton air conditioner in Watts. 5. lock supports an iron pendulum and another clock supports a brass pendulum. oth the clocks are accurate at 0 o. What will be difference in their readings after one day if the temperature is 40 o? α (steel ) =. 0 5 / 0 and α (brass) = 0 5 / 0 6. wo walls I and II of the same thickness are made of heterogeneous metals, as shown in fig. In what case will the coefficient of thermal conducitivity will be greater? 7. small blackened solid copper sphere of radius m is placed in an evacuated enclosure whose walls are kept at t what rate must energy be supplied to be sphere to keep its temperature constant at 7 0? σ = in S.I. units. nswers : Part -. (a) - melting, - vaporisation (b) L vap. = L fusion (c) slope α specific heat (d) hermal capacity in liquid state > hermal capacity in solid state o /7 gm 4. 35/9 KW sec W 8

2 Part -. open vessel contains 500 gm of ice at - 0 o. he mass of the container can be neglected. Heat is supplied to the vessel at the constant rate of 00 cal/ min for 00 minutes. Plot a curve showing the elapsed time as abscissa and the temperature as ordinate.. copper calorimeter of mass 00 gm contains 50 gm of water and 8 gm of ice in thermal equilibrium at atmospheric pressure. 00 gm of lead at a temperature of 00 o are dropped in the calorimeter. Find the final temperature if no heat is lost to the surrounding. c lead = 0.3 J/gm/ o, c u = 0.39 J/gm/ o. 3. t a temperature of 0 o, the volume of a certain glass flask, upto a reference mark on the stem of the flask, is exactly 00 cm 3. he flask is filled to this point with a liquid whose coefficient of volume expansion is. 0 3 / o, with both flask and liquid at 0 o. he cross-section of the stem is mm and can be considered constant. How far will the liquid rise or fall in the stem if the temperature is raised to 40 o? he coefficient of linear expansion of glass is / o. 4. (a) n aluminum vessel of volume 300 cc is completely filled with glycerine at 0 o. Find the mass of glycerine that will overflow when both are heated to 00 o, ρ (glycerine) at 0 o =.69 g/cc, γ (glycerine) = / o and α (l) = / o (b) glass vessel is partially filled with mercury and when both are heated together, the volume of the unfilled part of the vessel remains constant at all temperatures. Find the initial volume of mercury if the volume of glass vessel is 50 cm 3. α (glass) is / o, α (Hg) = / o. 5. glass flask contains 330 gm of mercury at 0 o, and 35 gm at 00 o. Find the coefficient of linear expansion for flask if the coefficient of cubic expansion of mercury is / o. 6. hree rods of material X and three rods of material Y are connected as shown in fig. ll the rods are of identical length and cross sectional area. If the end is maintained at 60 o, and the junction E at 0 o, calculate the temperatures of the junctions,,. he thermal conductivity of the rod X is 0.9 cal/ o /s/cm and that of Y is 0.46 cal/ o /s/ cm. 7. rod of length l with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as K = α/, where α is a constant. he ends of the rod are kept at temperatures and. Find the function (x), where x is the distance from the end whose temperature is, and the heat flow density. 8. wo chunks of metal with heat capacities and are interconneted by a rod of length l and crosssectional area S and fairly low heat conductivity k. he whole system is thermally insulated from the environment. t a moment t = 0, the temperature difference between the two chunks of metal equals ( ) 0. ssuming the heat capacity of the rod to be negligible, find the temperature difference between the chunks as a function of time. 9. constant electric current flows along a uniform wire with cross-sectional radius R and heat conductivity coefficient k. unit volume of the wire generates a thermal power ω. Find the temperature distribution across the wire provided the steady-state temperature at the wire surface is equal to 0. 8

3 0. n isosceles triangle is formed with a thin rod of length l and coefficient of linear expansion α as the base and two thin rods each of length l and coefficient of linear expansion α as the two sides. If the distance between the apex and the mid-point of the base remain unchanged as the temperature is varied show that l l = α α. n aluminum plate is fixed in a horizontal position has a hole of diameter d a = cm. steel sphere of diameter d s =.005 cm rests on this hole. ll the lengths refer to temperature = 0 o. he temperature of the entire system is slowly increased. t what temperature the steel plate cover the hole? α a = / o and α s = 0 6 / o. Petroleum is stored in a cylindrical tank of height h = 0 m. t a temperature t 0 = 0 o, the separation between the level of petroleum and the top of the tank is h = 50 cm. t what temperature t does petroleum overflows from the tank. he coefficient of cubic expansion of petroleum is γ = /K and the diameter of the steel tank is d = 6 m and its coefficient of linear expansion is α s =. 0 5 / o. 3. s a result of a temperature rise of 3 o, a bar with a crack at its centre buckles upward (fig). It the fixed distance L 0 = 3.77 m and the coefficient of linear expansion is / o, find x, the distance to which the centre rises. 4. rod is rotating about an axis passing through its one end and perpendicular to its length with a constant angular velocity ω. alculate the percentage change in the kinetic energy of the rod if the temperature of the rod is changed from 0 o to 50 o. α iron =. 0 5 / o. 5. he length of a copper rod is 00 cm when measured by a steel scale, both being at 0 o. What will be the reading of the scale when both are heated to 50 0? ssume that the scale is accurate at 0 o. α (steel ) =. 0 5 / o α (u) = / o 6. cylindrical metal can 0 cm high and 5 cm in diameter contains liquid helium at 4 K, at which temperature its heat of vepourisation is 0 J/gm. ompletely surrounding the helium can are walls maintained at a temperature of liquid nitrogen, 80 K, the intervening space being evacuated. How much helium is lost per hour? ssuming the radiant emittance of the helium can to be 0. that of a black body at 4 K. ssume only curved surface area of the cylinder. nswers : Part -. 0 o with 0. g ice 3. Raise.38 m g,.4cc / o o, 0 o, 0 o 7. x / l ( x) =, a l q= ln 8. (?) 0 e at ;a = 9. = o + (R -r ) ω/4k. = 8 o. t = 44. o cm + Sk l % cm 6..3 gm/hr 83

4 HE- II Part -. n ideal gas ( γ =.5) has a volume of 0 lt at a pressure of atm and temperature 300 K. It is adiabatically expanded to twice its original volume. alculate (a) no. of moles of the gas (b) the final temperature (c)the work done by the gas.. cylinder contains mole of oxygen at a temperature of 7 o. he cylinder is provided with a frictionless piston which maintains a constant pressure of atm on the gas. he gas is heated until its temperature rises to 7 o. (a) raw a diagram representing the process in the PV plane. (b) How much work is done by the gas? (c) On what is this work done? (d) How much heat was supplied to the gas? (e) What is the change in internal energy of the gas? (f) How much work should have been done if the pressure had been 0.5 atm? 3..0 moles of helium are initially at a temperature of 7 o and occupy a volume of 0 lt. he helium is first expanded at constant pressure until the volume is doubled, and then adiabatically until the temperature returns to its initial value. (a) raw a PV diagram (b) ompute the total heat supplied in the process (c) alculate the change in internal energy of the system. (d) What is the total work done by the gas? (e) What is the final volume? 4. n ideal gas having initial pressure P, volume V and temperature is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to /. (a) How many degrees of freedom do the gas molecules have? (b) Obtain the work done by the gas during theexpansion as a function ofthe initial pressure P and volume V? 5. wo perfect gases at absolute temperatures and are mixed. here is no loss of energy. Find the temperature of the mixture if masses of molecules are m and m and the number of molecules in the gases are n and n respectively. 6. What amount of heat is to be transferred to nitrogen in the isobaric heating process for that gas to perform the work.0 J? 7. wo moles of helium undergo a cyclic process as shown in figure. ssuming the gas to be ideal, calculate the following quantities in this process. (a) he net change in the heat energy. (b) he net work done. (c)he net change in the internal energy. (d) raw the P-V diagram. P atm atm 300 K 400 K 84

5 8. 3 moles of an ideal gas ( p = 7/ R) at pressure P and temperature is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally gas is compressed at constant volume to its original pressure P. (a) Sketch the P-V, P - and V - diagrams for the complete process. (b) alculate the net work done by the gas, and net heat supplied to the gas during the complete process. Part -. One mole of a monoatomic ideal gas is taken through the cycle shown : P : adiabatic expansion : cooling at constant volume : adiabatic compression : heating at constant volume he pressure and temperature at, etc. are denoted by P,, P, V etc. respectively. Given that = 000 K, P = (/3) P and P c = (/3) P. alculate the following quantities. (a) he work done by the gas in the process (b) he heat lost by the gas in the process (c) he temperature. (Given : (/3) /5 = 0.85).. n ideal gas is taken through a cyclic thermodynamic process through four steps. he amount of heat involved in these steps are Q = 5960 J. Q = 5585 J, Q 3 = 980 J, Q 4 = 3645 J, W = 00 J, W = 85 J, W 3 = 00 J, and W 4 respectively. (a)find the value of W 4. (b) What is the efficiency of the cycle? 3. horizontal insulated cylinder is provided with frictionless, non-conducting piston. On each side the piston is 50 l t of air at a pressure of atm and 73 K. Heat is slowly suppied to the air at the left hand side, until the piston has compressed the air on the right hand side of.5 atm. Find (a) the final temperature of the air on the right hand side ; (b) work done by the airon the right hand side ; (c) the final temperature of air ; (d) heat added to the air on the left hand side. 4. smooth vertical tube having two different sections is open from both ends and equipped with two pistons of different areas. Each piston slides within a respective tube section. mole of ideal gas is inclosed between the pistons tied with a nonstretchable thread. he cross-sectional area of the upper piston is S = 0 cm greater than that of the lower one. he combined mass of the two pistons is equal to m = 5.0 Kg.he outside air pressure is p 0 =.0 atm. y how many Kelvins must the gas between the pistons be heated so as to move the pistons through = 5.0 cm? P 0 P 0 5. Find the molar heat capacity of an ideal gas in a polytropic process Pv n = const. he adiabatic exponent of the gas is equal to γ. t what values of the polytropic constant n will the heat capacity of the gas be negative? 6. One mole of a certain ideal gas is contained under a weightless piston of a vertical cylinder at a temperature. he space over the piston opens into the atmosphere. What work has to be performed in order to increase isothermally the gas volume under the piston n times by slowly raising the piston? he friction of the piston against the cylinder walls is negligibly small. 85

6 7. he volume of one mole of an ideal gas with adiabatic exponent is varied according to the relation V = a/, where a is a contant. Find the amount of heat obtained by the gas in this process if the gas temperature is increased by. 8. gaseous mixture enclosed in a vessel of volume V. consists of one mole of a gas with γ = 5/3 and another gas with γ= 7/5 at a certain temperature. he relative molar masses of the gases and are 4 and 3 respectively. he gases and do not react with each other and are assumed to be ideal. he gaseous mixture follows the equation : PV 9/3 = constant, in adiabatic processes. (a)find the number of moles of the gas in the gaseous mixture. (b)ompute the speed of sound in the gaseous mixture at = 300 K (c) If is raised by K from 300 K. find the percentage change in the speed of sound in the gaseous mixture. (d) he mixture is compressed adiabatically to /5 of its initial volume V. Find the change in its adiabatic compressibility in terms of the given quantitities. 9. sample of kg of monoatomic Helium (assumed ideal) is taken through the process and another sample of kg of the same gas is taken through the process (see Figure). Given relative molecular mass of Helium = 4. (i) What is the temp.of Helium in each of the stages,, and? (ii) Is there any way of telling afterwards which sample of Helium went 0 4 N/m 0 through the process and which went through the process. Write Yes or No. (iii) How much is the heat involved in each of the processes and? V m 3 0. One mole of a diatomic ideal gas ( γ =.4) is taken through a cyclic process starting from point. he process is an adiabatic compression, is isobaric expansion. is an adiabatic expansion, and is isochoric. he volume ratios are V / V = 6 and V / V = and the temperature at is = 300 K. alculate the temperature of the gas at the points and and find the efficiency of the cycle. nswers Part -. (a) 0.4 (b). K (c) 583 J. (b) 83 J (c) Piston (d) 909 J (e) J (f) Same 3. (b).47 KJ (c) Zero (d).47 KJ (e) 3.4 lt 7. (a) 50.8 J (b) 50.8 J (c) zero 4. (a) 5 (b) PV w = γ ( ( 5.66) ) γ 5. n n + n + n 6. 7 J 8. R( log 8 -.5) Part J J., 500 K J, 0.08 J K, J., 00 K J; γ = K. 5. [R(n - )]/[(n - )(r - )]. Negative for < n < r. 6. R(n - - ln n) 7. R ( -γ )/(γ -) 8. (a) n = mol,(b) 40 ms -. (c) 0.67 (d) ( Pa - )(Km -3.)(V/) 9. (i) 0.8 K, K, 48. K, K, (ii) No. (iii) J, J K, 79.4 K.,

PHYS102 Previous Exam Problems. Temperature, Heat & The First Law of Thermodynamics

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