Total No. of Questions 12] [Total No. of Printed Pages 7 Seat No. [4162]-189 S.E. (Chemical Engineering) (Second Semester)EXAMINATION, 2012 THERMODYNAMICS-I (2008 PATTERN) Time : Three Hours Maximum Marks : 100 N.B. : (i) Answer three questions from Section I and three questions from Section II. (ii) Answers to the two Sections should be written in separate answer-books. (iii) (iv) (v) Neat diagrams must be drawn wherever necessary. Figures to the right indicate full marks. Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. (vi) Assume suitable data, if necessary. SECTION I 1. (a) A steel casting is in thermal equilibrium with a copper casting. The composite system of steel and copper casting undergoes adiabatic change. Show that under adiabatic conditions heat lost by one casting is equal to heat gained by the other casting if no work is exchanged between two castings. [8] P.T.O.
A spherical balloon of diameter 0.5 m contains a gas at 1 bar and 300K. The gas is heated and the balloon is allowed to expand. The pressure inside the balloon is directly proportional to the square of the diameter. What would be the work done by the gas when the pressure inside reaches 5 bar? [8] 2. (a) An elevator with a mass of 2500 kg rests at a level 10 m above the base of an elevator shaft. It is raised to 100 m above the base of the shaft, where the cable holding it breaks. The elevator falls freely to the base of the shaft and strikes a strong spring. The spring is designed to bring elevator to rest and by means of a catch arrangement to hold the elevator at the position of maximum spring compression. Assuming the entire process of be frictionless and taking g = 9.8 m/s 2, calculate : (i) Potential energy of elevator in its initial position; (ii) The work done in raising the elevator; (iii) The potential energy of elevator in its highest position relative to the base of shaft; (iv) The velocity and kinetic energy of the elevator just before it strikes the spring; (v) The potential energy of compressed spring. [10] [4162]-189 2
Explain : (i) Intensive and extensive properties; (ii) Steady state and equilibrium state. [6] 3. (a) An ideal gas undergoes the following sequence of mechanically reversible processes in a closed system : [12] (i) From an initial state of 343K and 1 bar, it is compressed adiabatically to 423 K; (ii) It is then cooled from 423 K to 343 K at constant pressure; (iii) Finally it is expanded isothermally to its original state. Calculate W, Q, E and H for each process and for the entire cycle. Take C 3 v = ( 2 ) R, C 5 ( 2 ) p = R. Explain PV diagram for a pure substance. [6] 4. An ideal gas is changed from P 1 = 1 bar and V 1 = 12 m 3 to P 2 = 12 bar and V 2 = 1 m 3 by the following mechanically reversible processes : (a) (c) (d) Isothermal compression; Adiabatic compression followed by cooling at constant pressure; Adiabatic compression followed by cooling at constant volume. Heating at constant volume followed by cooling at constant pressure. [4162]-189 3 P.T.O.
Calculate Q, W, E and H for each of these processes and sketch the paths of all processes on a single PV diagram. Take C p = (5/2)R and C v = (3/2)R. [18] 5. (a) Dry methane is burned with dry air. Both are at 25ºC initially. The flame temperature is 1300ºC. If the complete combustion is assumed, how much excess air is being used? The reaction is CH 4 + 2O 2 CO 2 + 2H 2 O. The standard heat of reaction is 8.028 10 5 J/mol of methane reacted. Mean molal specific heats of gases between 25ºC and 1300ºC are (J/mol.K) CO 2 = 51.66, H 2 O = 40.45, O 2 = 34.01, N 2 = 32.21. [8] It is required to calculate the standard enthalpy change of the reaction : C 2 H 4 (g) + H 2 O(g) C 2 H 5 OH(g) at several temperatures. For this purpose develop a general expression to calculate Hº T as a function of temperature. Standard heat of reaction at 298 K is 44.337 kj. Use the following data : Compound a b 10 3 c 10 6 C 2 H 4 4.196 154.565 81.076 H 2 O 28.850 12.055 C 2 H 5 OH 20.691 205.346 99.793 [8] [4162]-189 4
6. (a) Calculate the heat of the following gas phase reaction : H 2 + 1 2 O 2 H 2 O, Hº 298 = 242 kj. [10] if the reactants are at 473 K and the product is at 993 K. The specific heat C p = α + βt + V 2 T J/mol.K may be evaluated using the data given below : α β V H 2 29.09 8.374 10 4 2.0139 10 6 O 2 25.74 12.987 10 3 3.864 10 6 H 2 O 30.38 9.621 10 3 1.185 10 6 Explain different methods for rough estimation of latent heats of vaporisation for pure liquids. [6] Section II 7. (a) A Carnot engine operates between temperature levels of 600 K and 300 K. It drives a Carnot refrigerator, which provides cooling at 250 K and discards heat at 300 K. Determine a numerical value for the ratio of heat extracted by the refrigerator (cooling load) to the heat delivered to the engine (heating load). [9] Write a note on Clausius inequality. [7] 8. (a) A steel casting of mass 10 kg at 800ºC is quenched in 100 kg water at 30ºC in an insulated container. The heat capacities of steel and water are 0.461 and 4.23 kj/kg.k respectively. Calculate the change in entropy of steel and water. [7] [4162]-189 5 P.T.O.
Air an ideal gas with γ = 1.4, enters an adiabatic compressor at 25ºC and 0.1 MPa and leaves at 1 MPa and 330ºC. Calculate the isentropic efficiency of the compressor. [9] 9. (a) Discuss residual properties. [8] Show that : ( V T) P dh Cvd T VdP T = + dv ( V P) T [8] 10. (a) Derive Clausius-Clapeyron equation. [8] Prove that C p 2 TVβ Cv =. [8] K 11. (a) In northern states of India, the ambient atmosphere temperature greatly varies from season to season leading to uncomfortable conditions for living. In summer the temperature rises to as high as 42ºC and in winter it drops to as low as 0ºC. An engineer designs a device which can be used as refrigerating unit in summer and as a heat pump in winter to maintain the temperature of 25ºC inside the house in all seasons. The rate of energy losses as heat from the windows, walls and roof is estimated as 0.5 kw per degree Celsius temperature difference between the ambient atmosphere and the conditions inside the room. Estimate the minimum power required to operate the device in winter and in summer. [10] [4162]-189 6
With neat sketch explain the absorption refrigeration cycle. [8] 12. (a) In a vapor compression refrigeration system water is used as a refrigerant. Given that the evaporation temperature 277 K, the condensation temperature 307 K, efficiency of compressor 76% and the refrigeration rate = 1200 kw, determine the circulation rate of the refrigerant, the heat transfer rate in the condenser, the power requirement, the coefficient of performance of the cycle and the coefficient of performance of a Carnot refrigeration cycle operating between the same temperature levels. [14] Write a note on heat pump. [4] [4162]-189 7 P.T.O.