Thermodynamics Questions and Answers

3 A system containing air undergoes a change of state from pi v to p2 V2 whose values are 0 5 MPa 0 287 m kg and 0 1 MPa 1 435 m kg respectively The process undergone by the system is a isochoric b isobaric c isothermal d isentropic

40 A carnot engine has efficiency 25 It operates between reservoirs of constant temperatures with temperature difference of 80 K What is the temperature of the cold reservoir a 29 C c 27 C b 31 C d 33 C

neg d The collision between molecules is elastic 2 In the given V T diagram what is the relation between pressure P and P P P c P P P P T b P P d Data insufficient 8 Air i is he Ass the a 9 B 0 1 10

Find the change in the internal energy of 453 6 gr of O2 assume ideal gas heated from 20 C to 30 C at constant pressure of 1 atm Calculate the heat capacity at constant volume and internal energy of the system Specific heat capacity of O2 0 231 cal g K

c 18 2 c c d 20 2 c c 9 Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300K The piston A is free to move while that of B is held fixed The same amount of heat is given to the gas in each cylinder If the rise in temperature of the gas in A is 30K then the rise in temperature of the gas in B is a 30K b 18K c 50K d 42K

8 If quantity of heat 1163 4 J supplied to one mole of nitrogen gas at room temperature at constant pressure then the rise in temperature is a 54 K b 28 K c 65 K d 40 K

3 Heat is supplied to a diatomic gas at constant pressure The ratio between heat energy supplied and work done is y for diatomic gas 7 5 a 3 4 b 2 1 c 7 2 d 2 5 4 Two yessels 10

A sample of ideal gas of some mass is taken through the cycle process shown in the figure The temperature of the gas at state A is T 200K and at state C is T 1800K Choose the correct option P 0 B 3 V 9 PV I P V 3 k

An ideal gas undergoes a process in which its pressure P and volume V obey P V constant Bulk modulus of gas in the process is 1 P 2 Px P X 4 x p Volume pressure and temperature of an ideal gas aro K P and I respectively If mass of its 3

A constant volume gas thermometer shows pressure reading of 50 cm and 90 cm of mercury at 0 C and 100 C respectively When the pressure reading is 60 cm of mercury the temperature is 25 C 40 C 15 C 12 5 C

34 A thermoflask made of stainless steel contains serveral tiny lead shots If flask is quickly shaken up and down several times the temperature of lead shots a Increase b Decrease c Remains same d First increase then doo

a a 4 P V 3V V c 6 P V d 15 P Vo 0 19 For the process as shown below the heat supplied to the system is 30 kJ per cycle The efficiency of the cycle is P kPa a 40 8 2 O b 12 Po Vo 0 A 2 b 60 6 B C V m c 50 d 30

36 A carnot engine working between 300 K and 600 K has work output of 800 J sec The amount of heat energy supplied from the source of engine in each cycle is a 1600 J b 1750 J c 1609 J d 1681 J 7 A carnot engine

35 A carnot engine extract heat from water at 0 C and rejects it to room at 24 4 C The work required by the refrigerator for every 1 kg of water converted into ice L 336 kJ kg ice a 20 kJ c 19 kJ b 25 kJ d 30 kJ

V 19 For a certain mass of gas the isothermal curves between P 2 303 RT log and V at T and T temperatures are 1 and 2 as shown in figure then a T T T T b T T OT P P 2 T 2 T

d 0 028 x 106 If Qaf 80 cal W 60 cal and W 30 cal for the iaf curved path f i then value of Q for path f i will be PA a 50 cal 18 The P Y 1 a b 30 cal V c 30 cal d 50 cal

14 If Q E and W denote respectively the heat added change in internal energy and the work done in a closed cyclic process then which of these will follow 0 b AQ 0

One mole of ideal monoatomic gas at initial state a with pressure P and v is taken to a final state d with pressure through the path a b c d figure a b and c d are adiacbatic paths where as b c is isothermal with temperature To Find the work done by the gas in the process b c Given In e 1 e p and volume P d e Po Vole O 2RT ORT 4RT Po Vo V La

336 W Power t 60 Two liquids A and B are at 32 C and 24 C When mixed in equal masses the temperature of the mixture is found to be 28 C Their specific heats are in the ratio of 1 3 2 2 2 3 3 1 1 4 4 3

Q 1 In different experiments an ideal gas is expanded through i Isothermal ii Adiabatic iii Isobaric process 65 In which of the processes mentioned the internal energy of the gas may decrease

2 x 10 P Pa 1 x 10 D B C T 1 414 R The net work done on the gas in the cycle ABCDA is 2 276 R Foro 300 k Assume the gas to be ideal the work done on the gas in taking it from A to B is 1 200 R 2 300 R 3 400 R 4 500 R The work done on the gas in taking it from D to A is 2 414 R 500 k 3 690 R 3 1076 R 4 690 R 4 1904 R 2X107

j A manufacturer claims to have constructed an engine tha has an efficiency of 35 when operated between th Boiling point of water and the freezing point of water Is hi claim correct Justify your answer with calculations

An insulated container of gas has two chambers separated by an insulating partition One of the chambers has volu V and contains ideal gas at pressure p and temperature T The other chamber has volume V and contains ideal at pressure p and temperature T If the partition is removed without doing any work on the gas the final equilibr temperature of the gas in the container will be JAIEEE 20 T T P V p V P V T P V T PVT PVT P V p V 3 PVT PVT P V p V T T p V p V 4 P V T P V T

tate quid opy orn 4 If the ratio of specific heat of gas at constant pressure to that at constant volume is y the change in internal energy of mass of gas when the volume changes from V to V at constant pressure p is R 0 b pV d you Y 1 Y 1 Work done in an isothermal change depends upon Ller pu Y 1 12 a y 1 4 1 In the following p isothermals at T an 94

7 An ideal monoatomic gas undergoes a process in which its internal energy U and density p vary as Up constant The ratio of change in internal energy and the work done by the gas is 0 5x Find value of x

6 The internal energy of a gas is given by U 2pV It expands from Vo to 2Vo against a constant pressure Po The heat absorbed by the gas in the process is xpoVo Find value of x An ideal monoatomic gas undergoes in

1 V 11 Figure shows a parabolic graph between T and T temperature V Volume for a gas undergoing an adiabatic process If the ratio of rms velocity of molecules and speed of sound in the gas at the same temperature is n then find the value of n

3 Two identical containers joined by a small pipe initially contain the same gas at pressure po and absolute temperature To One container is now maintained at the same temperature while the other is heated to 2To The common pressure of the gases will be Po Find value of x 3 X

A glass mug contains 100 g coffee at 20 C If heat is added to it at the rate of 1 cal s how much time would it take for the coffee to heat up to 80 CE Scoffee 0 25 cal g C A 1 min B 5 min c 25 min

8 Rate of heat flow through a cylindrical rod is H Temperatures of ends of rod are T and T If all the difference remains same and rate of heat flow dimensions of rod become double and temperature H is 0 x Find value of x becomes H Then H

During which of the following thermodynamic process represented by PV diagram the heat energy absorbed by system may be equal to area under PV graph 1 3 PA A PA A B V B V 2 PA O A 4 All of these B V

An ideal rigid diatomic gas undergoes expansion at constant pressure when AQ heat is added to it What is the ratio of the change in the internal energy AU to the heat supplied AQ X 1 X 2 3 X 4 AU AQ AU AQ AU AQ AU AQ 3 5 7 1 9 57 2 3

5 An ideal gas of mass m in a state A goes to a another state B via three different processes If Q Q and Q3 denote the heat absorbed by the gas along three paths then A Q Q Q3 C Q Q Q3 243 B B Q Q Q3 D Q Q Q3

17 A diatomic gas undergoes a process represented by PV1 3 constant Choose the incorrect statement 1 The gas expands by absorbing heat from the surroundings 2 The gas cools down during expansion 3 The work done by surroundings during expansion of the gas is negative 4 None of these

Two identical masses of 5 kg each fall on a wheel from a height of 20 m The whee disturbs a mass of 4 kg water the rise in temperature of water will be 1 2 6 C 2 0 48 C 3 0 32 4 0 12 C

5 Point One pound of air with an initial temperature of 200 F is allowed to expand without flow between pressure of 90 and 15 psia If the air is undergoing a process that follows pVn c where n 1 what is the heat transferred in Btu Select the correct response

There are 7 gas molecules in a closed container The volume of the container increases by a factor of 3 in such a way that the temperature of the gas does not change What is the change in entropy AS 7 7 23 O 7 7 021 23 21 11 23

Example 3 16 A monatomic van der Waals gas is contained in a cylinder of molar olume 0 8 lit mol at a pressure of 36 atm If a 4 05 atm lit mol 2 b 0 037 lit mol nd R 0 082 atm lit K mol calculate internal pressure and temperature of the gas

A cylinder is made of perfectly thermally insulating material so that its contents are thermally isolated from the environment The cylinder contains an ideal gas It is closed with a piston that is free to move vertically but fits tightly such that no gas leaks out of the cylinder There is no friction between the piston and the cylinder walls Additional masses Ideal gas Cylinder with thermally insulating walls Initially there are some small masses on top of the piston Many additional small masses are then added one by one to the piston very slowly The process ends when all the small masses have been placed on top of the piston Which of the following statements are correct i The initial and final temperatures of the gas are the same ii The internal energy of the gas increases iii The energy transferred thermally to the gas during the process is zero i e Qto gas 0 O ii and iii O i only O All of the statements are correct O ii only O iii only O i and ii O i and iii None of these statements are correct

MATCHING LIST TYPE This section contains 4 questions each having two matching lists List 1 List II The options for the correct match are provided as A B C and D out of which ONLY ONE is correct Marking scheme 3 for correct answer 0 if not attempted and 1 in all other cases 15 In each situation of Column I a process A B Cis given for an ideal gas Match each situation of Column I with correct results in Column II Column I Column II B Volume Volume P Pressure P B C Temperature Temperature B Volume B T T C V V p Temperature increases Pressure first increases and then remains constant r Temperature first decreases and then increases s Pressure first decreases and then remains constant Volume A a p q b r s c p q d q B a p b p s c p q d q C a p b q s c qd qr D a p q b r c s d q

In Fig 20 25 where V23 3 00V n moles of a diatomic ideal gas are taken through the cycle with the molecules rotating but not oscil lating What are a p2 p b P3 P1 and c T3 T 1 For path 12 what are d WinRT e Q nRT f AEin nRT and g AS nR For path 23 what are h WinRT i Q nRT j AEint nRT k AS nR For path 3 1 what are 1 W nRT m Q nRT n Pressure 1 Adiabatic Isothermal 2 Volume 3 V V23 Figure 20 25 Problem 17

The diagram shows the adiabatic curve for n moles of an ideal gas The bulk modulus for the gas corresponding to the point P will be 1 SnRT 3V 5V 4V 31 2V Vo 2 nR 2 1 Tangent T 21 37 41 5T 3 nR 4 2nRT V

13 A 100 watt electric heating element is placed in a pan containing one liter of water Although the heating element is on for a long time the water though close to boiling does not boil When the heating element is removed approximately how long will it take the water to cool by 1 C Assume that the specific heat for water is 4 2 kilojoules kilogram C 20 s O 40 S O 60 s 130 s 200 s

Sin x 10 t x c 2 The sun delivers 104 W m of electromagnetic flux to the earth s surface The total power that is incident on a roof of dimensions 10 10 m will be a 104 W b 105 W c 106 W C 33 d 10 W 11

The following P V graph shows five different thermodynamics process of an ideal gas The processes numbered 1 and 3 are one of them adiabatic and the other isothermal Temperature of the gas increases in PA 1 1 124 3 Both 1 and 2 32 1 V 3

In a thermodynamic T law constant The heat given to the gas when p2 5 temperature of 4 moles of gas is raised from T to 2T is 1 8RT 2 4RT 3 16RT 4 Zero process helium gas obeys the

Figure shows three paths connecting points a and b A single force F does indicated work on the particle moving along each path in indicated direction On the basis of this information a 60 J 60 J 60 J b Force acting is conservative Only mechanical is there in the system Both 1 2 None of these

3 The molar heat capacity of a certain substance varies with temperature T as c a bT where a 27 2 J mol K 1 and b 4 x 10 3 J mol 1 K 2 Then the heat necessary to change the temperature of 2 moles of this substance from 27 C to 427 C is nearly 1 24 460 J 3 23 460 J 2 23 360 J 4 22 360 J

Q 15 0 336 m of gas at 10 bar and 150 C expands adiabatically until its pressure is 4 bar It is then compressed isothermally to its original volume Find the final temperature and pressure of the gas Also determine the change in internal energy Take cp 0 996 kJ kg K and cv 0 703 kJ kg K

The graph of pressure versus volume of a monoatomic ideal gas is as shown What is the internal energy of the system in state 1 and the heat given to the system during the process 4 to 1 Pressure Pa 1 2 3 15 5 3 20 6 5 4 7 9 543 3 Question Type Single Correct Type 21 2 4 1 2 3 4 5 6 Volume m