Thermodynamics Questions and Answers

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston as shown in the figure Initially the gas is at temperature T pressure P and volume V and the spring is in its relaxed state The gas is then heated very slowly to temperature T2 pressure P2 and volume V During this process the piston moves out by a distance x Ignoring the friction between the piston and the cylinder the correct statement s is are ch 3 f U URHU A Ka RHT fac fa zeng vur wu yg fdu da zuka L ZIRIN NH Iu T1 GId P1 27 3T2d7 V TR and 1 aga 2 P2 a 32 fchu a 1 34 ufku aa Mz Grazza am daa h geq qdu c aqua Hd A 2 2 A If V 2V and T2 37 then the energy stored in the spring is P V 2 2 T 37 u a Gaf P 0000000 D Correct Answer B in internal energy is 3P V If V 2V and T 3T then the change 2 1 37 3 Correct Answer C done by the gas is P V 3 3 T2 47 ada ga ku nu 1 of PV Correct Answer If V 3V and T 4T then the work If V 3V and T2 47 then the heat 17 D V supplied to the gas is

24 An ideal H gas undergoes a isothermal process according to the P V diagram shown The total heat given to the gas is nearly e IT B 3 14 X 211 210 P 2P Po 1 POV In2 2 2D VIn 2 A V B 2V V 2 2P V In2 1 1R InSt

A gas at state A changes to state B through path I and II shown in figure The change in internal energy is AU and AU2 respectively Then P 1 AU AU2 I 2 AU AU II V Question Type Single Correct Type B

21 The equation of a state of a gas is given by p V b nRT 1 mol of a gas is isothermally expanded from volume V to 2V the work done during the process is RT 2V b a RT In V b c RT ln V b 2V b b RT In d RT ln V b V V V b

7 Two pistons can move freely inside a horizontal cylinder having two sections of unequal cross sections The pistons are joined by an inextensible light string and some gas is enclosed between the pistons On heating the system the piston will a move to the left b move to the right c remain stationary d a or c depending upon the initial pressure of the gas

19 The figure shown two paths for the change of state of a gas from A to B The ratio of molar heat capacities in path 1 and path 2 is a 1 c 1 P A 2 1 b 1 d data insufficient manner that its B V

One mole of monatomic gas is brought from state A to state B The initial temperature at A is T The temperature at B will be A T B 2To C 3T D 4T 11 A RT 2 7 C RT 2P0 Po In the above question heat absorbed along the path ACB is A 2RT APT Vo IC B RT 0 D RT B 2Vo V In question the heat absorbed in going from A to B is B 6RT D 9DT 2

consider the following statements 40 In P a I only e II and III A D B C in the figure 12 2 V I Area ABCD Work done on the gas II Area ABCD Net heat absorbed III Change in the internal energy in cycle 0 Which of these are correct s X b II only d I II and III M 1 gan is

124 The temperature of 5 moles of a gas at constant volume is changed from 100 C to 120 C The change in internal energy is 80J The total heat capacity of the gas at constant volume will be in Joule Kelvin is 1 8 24 3 0 8 x2 4 0 4

14 The p V diagram of 2 g of helium gas for a certain process A B is shown in the figure What is the heat given to the gas during the process A B a 4p Vo c 3p V b 6poVo d 2p Vo P 2PO PO A 1 I 1 Vo W 1 B V 2V0 Po 2P

An ideal mono atomic gas is undergoing a cyclic process as shown in the fig then choose the correct statement A B C D 3Po P Po To B 2To Work done by gas in process CA is negative Heat is rejected by the system in process BC Work done by gas in the cyclic process is positive Internal energy of the gas decreases in the process AB T

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mas M The piston and cylinder have equal cross sectional area A When the piston is in equilibrium the volume of the gas is Vo and its pressure is Po The piston is slightly displaced from th equilibrium position and released Assuming that the system is completely isolated from it surrounding the piston executes a simple harmonic motion with frequency 2013 1 3 1 V MP 2 A y 1 MVo 2 A 1 A yPo 2T MVO 1 AyP

1 b an ideal Fermi gas d an ideal inert gas where v is th The equation of state of a dilute gas at very high temperature is described by KBT V volume per particle and B T is a negative quantity One can conclude that this is a property of a a van der Waals gas c an ideal Bose gas

48 When an air bubble rises from the bottom to the surface of a lake its radius becomes double Find the depth of the lake Given that the atmospheric pressure is equal to the pressure due to a column of water 10 m high Assume constant temperature and disregard surface tension a 30 m c 70 m b 40 m d 80 m

Consider a thermodynamic system which goes from i to f through the process shown in figure here Then work is done K Volume 6 By the system through out the path iABf By the system for path IAB and on the system for path Bf By the system for path IA and on the system for path ABf On the system throughout the path ABf

59 One mole of a gas expands with temperature T such that its volume V kT where k is a constant If the temperature of the gas changes by 60 C then the work done by the gas is a 120R b R ln 60 c kR ln 60 d 60kR

1 A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heat y It is moving with speed v and it suddenly brought to rest Assuming no heat is lost to the surroundings its temperature increases by a c Y 1 Mv K 2YR Y 1 Mv K 2R b YMv 2R d K x 1 2 y 1 R Mv K

61 Une mole of an ideal gas with heat capacity at constant pressure C undergoes the process T To aV where To and a are constants If its volume increases from V to V the amount of heat transferred to the gas is 2 V V a Cp RT In b aCp V V RT In c aC V V RT In AYAAN V V V V d RT InV 2 aC V V 0 V

Q13 In an isobaric expansion 200 J of work are done by the gas The gas pressure is 0 80 atm and it was originally at 20 0 L If the internal energy of the gas increased by 100 in the expansion how much heat does the gas absorb O A 50 J O B 100 J O C 250 J O D 300 J

One mole of a van der Waals gas obeying the equation P V V b RT PA P undergoes the quasi static cyclic process which is shown in the P V diagram The net heat absorbed by the gas in this process is A P P V V C P P V V P V V B P P V V D P P V V

67 An ideal gas is taken through a cyclic thermodynamic process through four steps amounts of heat involved in these steps are 5960 J Q 5585 J Q3 2980 J and Q4 3645 J respectively The corresponding works involved are W 2200J Q W 2200J W 825J W3 1100 J and W respectively E What is the efficiency of the cycle a 10 82 b 11 42 c 9 32 d 5 82 The atomic gas A C

58 At 27 C two moles of an ideal monoatomic gas occupy a volume V The gas expands adiabatically to a volume 2V Which of the following option correct a Final temperature of the gas is 189 K b Change in its internal energy 2767 235 c The work done by the gas during the process is 2767 235 d All are correct

To Atmosphere A non conducting vessel containing n moles of a diatomic gas is fitted with a conducting piston The cross sectional area thickness and thermal conductivity of piston are A and K respectively The right side of the piston is open to atmosphere is maintained at temperature To Heat is quasi statically supplied to the gas by means of an electric heater at a constant rate q Find temperature of the a function of time

Acaront reversible engine converts 1 6 of heat work When the temperature of the sink is red by 62 K the efficiency of carnot s cycle beco 1 3 The temperature of the source and sink be 1 372 K 310 K 2 181 K 150 K 3 472 K 410 K 4 None of these

A thermodynamic cyclic process abcd has two isothermals one isobaric and one isochoric process as shown on pressure volume P V diagram by volume The same cyclic process temperature V T diagram is best represented 91 2 a Pa a T Medic T Divisions

Two solid bodies of equal masses are heated at a uniform rate under identical conditions The change in temperature taken on Y axis in the two cases is shown graphically 100 80 60 40 AT A 20 1234 5 6 7 8 9 10 Time A The ratio of their specific heats in solid state is 1 3 B The ratio of their specific heats in solid state is 1 2 C The ratio of their latent heats is 2 1 D The ratio of their latent heats is 4 1 SECTION

be decrease by 50j 52 100 mol of an ideal gas is heated from 10 to 20 C keeping its i volume constant ii pressure constant Let AU and AU denote the change in the internal energy of the gas due to process i and ii respectively Then which of the following shall be a AMU 2012 true a AU AUb c AUa AUb b AU AU a d AU AU 0 a b

A mass less piston divides a closed thermally insulated cylinder into two equal parts One part contains m 28 gram of nitrogen at temperature To At this temperature one third of molecules are dissociated into atoms and the other pa is evacuated The piston is released and the gas fills the whole volume of the cylinder Then the piston is slowly displaced back to its initial position The increase in internal energy of the gas is Neglect further dissociation of molecules during motion of the piston A 2 1 RTO C 2 1 RTO B 2 1 RTO D 2 1 RTO

14 In thermodynamic processes correct match of column I with column ll is Column l Type of process a Isothermal b Isobaric c Isochoric NCERT Pg 306 Column II Feature i Volume constant ii Pressure constant iii No heat flow between system and surroundings

of the following is incorrect NCERT Pg 315 statement 1 Free expansion of a gas is irreversible process 2 A thermodynamic process is reversible if process can be turned back so that both system and surrounding return to their original states 3 No process is possible whose sole result is transfer of heat from a colder object to hotter object 4 The efficiency of an ideal heat engine is unity

3 A reversible cyclic heat engine absorbs 900 joule of heat from source If 400 J of heat is released to the sink what is the efficiency o the engine NCERT Pg 314 1 2 3 0 0 2 3 4

10P N m 1 5J 2 10J 3 15J 4 20 J Heat energy absorbed by a system in going 19 fengur through a cyclic process shown in figure is V litre La 30 10 10 10P N m 1 5J 2 10J 3 15J 4 20 J yandan 30 P kPa V litre 30 10 10 30 P kPa

A thermometer is moved from a room where the temperature is 81 F to a freezer where the temperature is 15 F After 30 seconds the thermometer reads 59 F Let T t denote the temperature in Fahrenheit at time t in seconds Using Newton s cooling law T t k T t T t to answer the questions a Write a differential equation for T t The only unknown should be T t T t B b What does the thermometer read after 2 minutes c Compute the limit lim T t 100 F

The human heart discharges 75 cc of blood through the arteries at each beat against an average pressure of 10 cm of mercury Assuming that the pulse frequency is 72 per minute calculate the rate of working of heart in watt density of mercury 13 6 g cc and g 9 8 m s

Three highly conducting concentric spherical shells acting as black body of radii nr2 and r3 are kept in vacuum The region between the shells is evacuated and they can exchange energy only by radiation Inside the innermost shell there is a heater of constant power P In steady state o Stefan s constant 1 2 3 4 Temperature of outermost shell is Temperature of middle shell is P 4TO 1 4 P 4TO Temperature of innermost shell is 1 4 1 1 4 1 4 P 4RO If both outer and middle shell were removed the temperature of innermost shell would decrease 1 4

The spectrum of a black body at 7 C is as shown in the figure The area under the curve is A The corresponding area at 133 C will be A 1 1 1 2 A Spectral Intensity 7 C wavelength 2 A 4

56 Steam at 100 C is allowed to pass into a vessel containing 10 gm ice and 100 gm of water at 0 C until all the ice is melted and the temperature is raised to 40 C Neglecting water equivalent of the vessel the approximate amount of steam condensed is 4 9 gn 3 15 gm 2 18 gm 4 21 gm

If pressure P is inversely proportional to volume V then a PV Constant b V x 1 1 a e are correct 2 c d are correct c PV P V 3 a b c are correct d Constant 4 All of these

MT 02 erator the ejects Re 15 7 1 1 1 00 work mergy e is 49 A gas is compressed isothermally to half its initial volume The same gas is compressed separately through an adiabatic process until its volume is again reduced to half Then a Compressing the gas isothermally will require more work to be done b Compressing the gas through adiabatic process will require more work to be done c Compressing the gas isothermally or adiaba tically will require the same amount of work d Which of the case whether compression through isothermal or through adiabatic process requires more work will depend upon the INEET 16

Sir please explain the method of solving this question in d tail 14 A gas is taken from state 1 to state 2 along the path shown in V P diagram If 70 cal of heat is extracted from the gas in the process then V m 3 10 1 10 2 2 10 5 10 P N m 1 Internal energy of gas increases by 224 I 2 Internal energy of gas decreases by 224 J 3 Internal energy remains constant 4 Internal energy of gas decreases by 264 J

el 11 53 The power radiated by a black body is P and it e radiates maximum energy at wavelength 2 If the temperature of the black body is now changed so that it radiates maximum energy at wavelength the power radiated by it becomes nP The value of n is 3 S 4 a c 3 4 256 81 b d 81 256 43 INEET 18

113 The following are the P V diagrams for cyclic processes for a gas In which of this process is not heat absorbed by the gas fata V 1 P 3 10 P 2 V 4 V A 1

3 One mole of an ideal gas undergoes a process T 300 2V where 7 is temperature and Vis volume If volume of gas increases from 2 m to 4 m then work done by the gas in this process will be 1 300R In2 2 2 2ln2 3 300R In2 4R 4 300R In2 4R 4 The temperature of a room heated by a heater is

An ideal gas undergoes adiabatic process according to the law TV1 2 constant If the gas is at pressure P and temperature T at a certain instant the value of the adiabatic modulus of elasticity is 1 P 2 3 2 P 5

Mete 58 A metallic conductor at 10 C connected in the left gap of meter bridge gives balancing length 40 cm When the conductor is at 60 C the balancing point shifts by cm temperature coefficient of resistance of the material of the wire is 1 220 C 1 4 8 2 10 3 15 4 7

Consider t non interacting classical particles are in a system It is one dimension harmonic potential The form of energy of the system is V x ox o is constant Fi 1 the partition function of the system at temperature T where B KT

A closed rigid tank filled with water vapor initially at 20 MPa 520 C is cooled until its temperature reaches 400 C Using the compressibility chart determine a the specific volume of the water vapor in m kg at the initial state b the pressure in MPa at the final state Compare the results of parts a and b with the values obtained from the superheated vapor table Table A 4 ad RT Z 1 0 0 5 0 Fig E3 7 N Z UR 1 2 U R 1 1 0 5 PR PR2 TR 1 3 TR 1 2 TR 1 05 1 0

The efficiency of the reversible heat engine is 11 and that of irreversible heat engine is n Which of the following is correct 1 1 and n 1 3 n 1 and n 1 2 1 1 4 1 1

n testprep answer key user test id 842749 Three Carnot engines operate in series between a heat source at a temperature f and a heat sink at temperature T see figure There are two other reservoirs at temperature t and T3 as shown with T T T3 T4 The three engines are equally efficient if T Option 2 0 2 T T3 T4 Option 1 T 1 T 2 T3 T T 1 3 T T 3 T3 1 T 3 Option 3 T 1 T2 T T7T T3

One mole of a monoatomic ideal gas undergoes a cyclic process as shown in the figure where V is the volume and T is the temperature Which of the statements below is are true TA IA B II IV III A Process I is an isochoric process os In process II gas absorbs heat In process IV gas releases heat Processes I and III are not isobaric V