thermo questions

Thermodynamics

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2 THERMODYNAMICS www.madeeasy.in Copyright : MADE EASY

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata PS-ME16

Q.1Q.1Q.1Q.1Q.1 An insulated rigid vessel contains a mixture of fuel and air. The mixture is ignited by a minute spark. Thecontents of the vessel experience(a) Increase in temperature, pressure and energy(b) Decrease in temperature, pressure and energy(c) Increase in temperature and pressure but no change in energy(d) Increase in temperature and pressure but decrease in energy

Q.2Q.2Q.2Q.2Q.2 A rectangular box as shown in figure has a partition which slides without friction along the length of the box.

Initially the 2 chambers of box has 1 kg each of an ideal gas 53

= at a pressure P0, volume V0 and

temperature T0. The chamber on the left is slowly heated by an electric heater. The walls of the box and thepartition is thermally insulated. The gas in the left chamber expands pushing the partition until the final

pressure in both the chambers is 0243P

32. Determine the final temperature of the gas in each chamber in

terms of T0, P0, V0 and W.D by the gas in the right chamber.

Q.3Q.3Q.3Q.3Q.3 A fluid contained in a piston cylinder machine passes through a complete cycle of 4 processes. The sumof all the heat transfers during cycle is 170 kJ/cycle. The system completes 100 cycles/min. Complete thefollowing table and also find the net work in kW.

ProcessProcessProcessProcessProcess Q (kJ/min)Q (kJ/min)Q (kJ/min)Q (kJ/min)Q (kJ/min) W (kJ/min)W (kJ/min)W (kJ/min)W (kJ/min)W (kJ/min) E (kJ/min)E (kJ/min)E (kJ/min)E (kJ/min)E (kJ/min)a - b 0 2170 b - c 21000 0 c - d 2100 36600d - a

Q.4Q.4Q.4Q.4Q.4 When the valve of the evacuated bottle as shown in figure is opened atmospheric air rusher into it. If theatmospheric pressure is 101.325 kPa and 0.6 m3 of air (measured at atmospheric condition) enters into thebottle, calculate the W.D. by air.

Thermodynamics



Q.5Q.5Q.5Q.5Q.5 The contents of a well insulated tank are heated by a resistor of 23 in which 10A current is flowing.Consider the tank along with its contents as a thermodynamic system. The work done by the system andthe heat transfer to the system are positive. The rates of heat (Q), work (W) and change in internal energy(U) during the process in kW are(a) Q = 0, W = 2.3, U = +2.3 (b) Q = +2.3, W = 0, U = +2.3(c) Q = 2.3, W = 0, U = 2.3 (d) Q = 0, W = +2.3, U = 2.3

Q.6Q.6Q.6Q.6Q.6 A rigid insulated tank with a supply line through which an ideal gas (with constant specific heats CP = 0.945and CV = 0.690) passes at 1 MPa, 350C. A valve connected with the supply line is opened and the tank ischarged until the final pressure inside the tank reaches 1 MPa. The final tempeature inside the tank.

(a) is greater than 350C(b) is less than 350C(c) is equal to 350C(d) may be greater than, less than, or equal to 350C, depending on the volume of the tank

Q.7Q.7Q.7Q.7Q.7 A rigid tank of volume 0.5 m3 is initially evacuated. A tiny hole develops in the wall, and air from thesurroundings at 1 bar, 21C leaks in. Eventually the pressure in the tank reaches 1 bar. The processoccurs slowly enough that the heat transfer between the tank and the surroundings keep the temperatureof the air inside the tank constant at 21C. Determine the amount of heat transfer.

Q.8Q.8Q.8Q.8Q.8 A stationary system consisting of 2 kg of fluid

CP = 1.005 kJ/kgK

CV = 0.718 kJ/kgK

pv = 0.287 (t + 273)

u = 196 + 0.718 t (u in (kJ/kg)

expands in an adiabatic process according to pv1.2 = constant. The initial conditions are 1 MPa and200C, and the final pressure is 0.1 MPa. Find W and E for the process. Why is the work transfer notequal to pdV .

Q.9Q.9Q.9Q.9Q.9 A reversible heat engine operates between 600C and 40C. This engine drives a reversible refrigeratoroperating between 40C and 18C. Still there is a net work output of 370 kJ, while the heat required by theengine is 2100 kJ. Determine the cooling effect (Desired effect) of the refrigerator.



Q.10Q.10Q.10Q.10Q.10 A closed system executes a reversible cycle 1-2-3-4-5-6-1 consisting of 6 process

1-2: Constant temperature (500 K) heat addition of 1000 kJ

2-3: Adiabatic expansion, temperature decreases from 500 k to 400 K

3-4: Constant temperature, system receivers 800 kJ of heat

4-5: Adiabatic expansion, temperature decreases from 400 K - 300 K

5-6: Constant temperature (300 K) heat rejection

6-1: Adiabatic compression

(i) Represent the cycle on T-S and P-V diagram

(ii) Find net workdone and also find the efficiency.

Q.11Q.11Q.11Q.11Q.11 Consider a steady heat transfer through a 5 m 7 m brick wall of a house of thickness 30 cm. On a day

when the temperature of outdoors is 0C, the house is maintained at 27C. The temperature of the inner and

outer surfaces of the brick wall are 20C and 5C, and the heat transfer through the wall is 1035 W. Determine

the rate of entropy generation in the wall and the rate of total entropy generation associated with this heat

transfer.

Q.12Q.12Q.12Q.12Q.12 A heat engine receivers heat from a source at 1200 K at a rate of 500 kJ/s and rejects the waste to a

medium at 300 K. The power output of the engine is 180 kW. Determine the irreversibility rate for this

process.

Q.13Q.13Q.13Q.13Q.13 A solid aluminium sphere of 0.1 m diameter initially at 200C is allowed to cool to ambient temperature of

25C. The density of aluminium is 2700 kg/m3 and the specific heat is 0.9 kJ/kgK. Then find the irreversibility

in kJ.

Q.14Q.14Q.14Q.14Q.14 A mixture of ideal gases consist of 3 kg of N2 and 5 kg of CO2 at a pressure of 300 kPa and at temperature

of 20C (Take of CO2 = 1.286 and of N2 = 1.4). Find(i) Mole fraction of each component

(ii) Equivalent molecular weight of mixture

(iii) Equivalent gas constant

(iv) Partial pressure of each constituent

(v) Total volume of the mixture

(vi) CP and CV of the mixture

(vii) Density of the mixture

(viii) If this mixture is heated at constant volume to 40C, find changes in U, H, S of the mixture

(ix) of CO2 = 1.286 and of N2 = 1.4Q.15Q.15Q.15Q.15Q.15 Two vessels A and B both containing nitrogen are connected by a valve which is opened to allow the

contents to mix and to achieve an equlibrium temperature of 300 K. Before mixing vessel A contains 14 kg

of N2 at 50C and at a pressure of 1.5 MPa. The vessel B contains 2.5 kg of N2 at 0.6 MPa and at a

temperature of 20C. Calculate the final equilibrium pressure and the amount of heat transferred to the

surroundings ( = 1.4).



Q.16Q.16Q.16Q.16Q.16 A closed cylinder of 0.25 metre diameter is fitted with a light frictionless piston. The piston is retained inposition by a catch in the cylinder wall and the volume on one side of the piston contains air at apressure of 750 kN/m2. The volume on the other side of the piston is evacuated. A helical spring ismounted coaxially with the cylinder in this evacuated space to give a force of 120 N on the piston in thisposition. The catch is released and the piston travels along the cylinder until it comes to rest after a strokeof 1.2 m. The piston is then held in its position of maximum travel by a ratchet mechanism. The spring forceincreases linearly with the piston displacement to a final value of 5 kN. Calculate the work done by thecompressed air on the piston.

Q.17Q.17Q.17Q.17Q.17 A tank containing 45 kg of water initially at 45C has one inlet and one exit with equal mass flow rates.Liquid water enters at 45C and a mass flow rate of 270 kg/h. A cooling coil immersed in the waterremoves energy at the rate of 7.6 kW. The water is well mixed by a paddle wheel with a power input of 0.6kW. The pressure at inlet and exit are equal. Ignoring changes in KE and PE, prove that the variation ofwater temperature with time is (T= 318 22(1 e6t).

Where, T is temperature in kelvin and t is time in hours.

Q.18Q.18Q.18Q.18Q.18 A heat engine operates between the maximum and minimum temperatures of 671C and 60C respectively,with an efficency of 50 % of the appropriate Carnot efficiency. It drives a heat pump which uses river waterat 4.4C to heat a block of flats in which the temperature is to be maintained at 21.1C. Assuming that atemperature difference of 11.1C exists between the working fluid and the river water, on the one hand, andthe required room temperature on the other, and assuming the heat pump to operate on the reveresedCarnot cycle, but with a COP of 50 % of the ideal COP, find the heat input to the engine per unit heat outputfrom the heat pump. Why is direct heating thermodynamically more wasteful?

Q.19Q.19Q.19Q.19Q.19 A reversible engine works between three thermal reservoirs, A, B and C. The engine absorbs an equalamount of heat from the thermal reservoirs A and B kept at temperatures TA and TB respectively, andrejects heat to the thermal reservoir C kept at temperature TC. The efficiency of the engine is times theeffciency of the reversible engine, which works between the two reservoirs A and C. Prove that

A A

B C

T T(2 1) 2(1 )

T T= +

Q.20Q.20Q.20Q.20Q.20 A heat pump is to be used to heat a house in winter and then reversed to cool the house in summer. Theinterior temperature is to be maintained at 20C. Heat transfer through the walls and roof is estimated to be0.525 kJ/s per degree temperature difference between the inside and outside. (a) If the outside temperaturein winter is 5C, what is the minimum power required to drive the heat pump? (b) If the power input is thesame as in part (a), what is the maximum outer temperature for which the inside can be maintained at20C?

Q.21Q.21Q.21Q.21Q.21 One kg of ice at 5C is exposed to the atmosphere which is at 20C. The ice melts and comes into thermalequilibrium with the atmosphere. (a) Determine the entropy increase of the universe. (b) What is the minimumamount of work necessary to convert the water back into ice at 5C? cp of ice is 2.093 kJ/kg K and thelatent heat of fusion of ice is 333.3 kJ/kg.



Q.22Q.22Q.22Q.22Q.22 Calculate the entropy change of the universe as a result of the following processes:

(a) A copper block of 600 g mass and with Cp of 150 J/K at 100C is placed in a lake at 8C.(b) The same block, at 8C, is dropped from a height of 100 m into the lake.(c) Two such blocks at 100 and 0C are joined together.

Q.23Q.23Q.23Q.23Q.23 A 50 ohm resistor carrying a constant current of 1 A is kept at a constant temperature of 27C by a streamof cooling water. In a time interval of 1 s, (a) what is the change in entropy of the resistor?(b) What is the change in entropy of the universe?

Q.24Q.24Q.24Q.24Q.24 A thermally insulated 50-ohm resistor carries a current of 1 A for 1 s. The initial temperature of the resistoris 10C, its mass is 5 g and its specific heat is 0.85 J/g K. (a) What is the change in entropy of the resistor?(b) What is the change in entropy of the universe?

Q.25Q.25Q.25Q.25Q.25 Liquid water of mass 10 kg and temperature 20C is mixed with 2 kg of ice at 5C till equilibrium isreached at 1 atm pressure. Find the entropy change of the system. Given: cp of water = 4.18 kJ/kg K,cp of ice = 2.09 kJ/kg K and latent heat of fusion of ice = 334 kJ/kg.

Q.26Q.26Q.26Q.26Q.26 A lead storage battery used in an automobile is able to deliver 5.2 MJ of electrical energy. This energy isavailable for starting the car.

Let compressed air be considered for doing an equivalent amount of work in starting the car. The compressedair is to be stored at 7 MPa, 25C. What is the volume of the tank that would be required to let thecompressed air have an exergy of 5.2 MJ? For air, pv = 0.287 T, where T is in K, p in kPa, and v in m3/kg.

Q.27Q.27Q.27Q.27Q.27 A Carnot cycle engine receives and rejects heat with a 20C temperature differential between itself and thethermal energy reservoirs.The expansion and compression processes have a pressure ratio of 50. For 1 kgof air as the working substance, cycle temperature limits of 1000 K and 300 K and T0 = 280 K, determinethe second law efficiency.

Q.28Q.28Q.28Q.28Q.28 Energy is received by a solar collector at the rate of 300 kW from a source temperature of 2400 K. If 60 kWof this energy is lost to the surroundings at steady state and if the user temperature remains constant at600 K, what are the first law and the second law efficiencies? Take T0 = 300 K.

Q.29Q.29Q.29Q.29Q.29 Argon enters an insulated turbine operating at steady state at 1000C and 2 MPa and exhausts at 350 kPa.The mass flow rate is 0.5 kg/s and the turbine develops power at the rate of 120 kW. Determine (a) thetemperature of the argon at the turbine exit, (b) the irreversibility of the turbine, (c) the second law efficiency.Neglect K.E. and P.E. effects. Take T0 = 20C, p0 = 1 bar.

Q.30Q.30Q.30Q.30Q.30 Steam enters a 15 cm diameter horizontal pipe as saturated vapour at 5 bar with a velocity of 10 m/s andexit at 4.5 bar and a quality of 0.95. Heat is transferred to surroundings at 300 K from the pipe surfacewhich is at an average temperature of 400 K. Under the steady state operation conditions, determine(i) the exit velocity.(ii) the rate of heat transfer from pipe surface in kW.(iii) the rate of entropy production in kW/K, for the control volume comprising of only pipe and its contents

and(iv) the rate of entropy production for the enlarged control volume that includes pipe, its contents and the

immediate surroundings.



Properties of steam at saturation condition:

p bar tsat C

Sp. volume,m /kg3

Sp. enthalpy,kJ/kg

Sp. entropykJ/kg-K

147.934.5

Liquid( )Vf

0.001088

Vapour( )Vg

0.4140

Liquid(h )f

623.5

Vapour( )hg

2744

Liquid(s )f

1.8207

Vapour(s )g

6.8565

151.865.0 0.001093 0.3749 640.0 2749 1.8607 6.8213

Q.31Q.31Q.31Q.31Q.31

2

3

1

A geothermal supply of hot water at 500 kPa, 150C is fed to an insulated flash evaporator at the rate of 1.5kg/s. A stream of saturated liquid at 200 kPa is drained from the bottom of the chamber and a stream ofsaturated vapour at 200 kPa is drawn from the top and fed to a turbine. Find the rate of entropy generationin the flash evaporator. Properties of water are given in the Table below:

p, kPa t, C h1, kJ/kg s1, kJ/kg-K sv, kg/kg-K

200

500

500

120.20

151.83

150.00

504.68

640.68

632.18

hv, kJ/kg

2706.63

2746.60

1.5300

1.8603

1.8417

7.1271

6.8202

( )tsat

( )tsat



ThermodynamicsPractice Questions

ANSWERS

15.15.15.15.15. P = 1168 kPa

Q = 226 kJ16.16.16.16.16. (3.07 kJ)

17.17.17.17.17. (T = 318 22 [1 exp(6t)])

18.18.18.18.18. 0.79 kJ/kJ heat input

19.19.19.19.19. A AB C

T T(2 1) 2(1 )

T T= +

20.20.20.20.20. (a) 403 W, (b) 35.4C

21.21.21.21.21. 0.0949 kJ/K, 28.25 kJ

22.22.22.22.22. (a) 6.69 J/K, (b) 2.095 J/K, (c) 3.64 J/K

23.23.23.23.23. (a) 0, (b) 0.167 J/K

24.24.24.24.24. (a) 0.173 J/K, (b) 0.173 J/K)

25.25.25.25.25. 104.5 J/K

26.26.26.26.26. 0.228 m3

2727272727..... 0.965

28.28.28.28.28. 0.80, 0.457

29.29.29.29.29. (a) 812 K, (b) 18.87 kW, (c) 86.4 %

30.30.30.30.30. (i) C2 =10.491 m/s(ii) Q = 52.181 kW

(iii) genS = 0.02939 kW/K

(iv) genS = 0.0722 kW/K

31.31.31.31.31. 17 W/K

2.2.2.2.2. TR = 2.25 T0TL = 12.397 T0W = 1.875 P0V0

5.5.5.5.5. (a)(a)(a)(a)(a)

6.6.6.6.6. (a)(a)(a)(a)(a)

7.7.7.7.7. Q = 50 kJ

8.8.8.8.8. W = 216.66 kJ

9.9.9.9.9. 4295.33 kJ

10.10.10.10.10. Wnet = 1000 + 800 1200 = 600 kJ

= supp

W 600 1Q 1800 3

= =

11.11.11.11.11. gens = 0.191 W/k

Total gens = 0.341 W/k

12.12.12.12.12. 195 kW

13.13.13.13.13. 47.49 kJ

14.14.14.14.14. (i) XN2 = 0.4853, XO2

= 0.5147

(ii) Me = 36.24

(iii) Re = e

R0.2294

M=

(iv) PN2 = 145.59 kPa, PCO2

= 154.41 kPa

(v) V = 1.789

(vi) CPe = 0.9206, CVe

= 0.6912

(vii) = 4.47 kg/m3(viii) U = 110.592, H = 147.296(ix) s = 0.365

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