Thermodynamics (Physics)

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is 4 cm2. The gas is heated slowly to raise the temperature by 1.2 °C during which the piston moves by 25 mm. The amount of heat supplied to the gas is J. (Atmospheric pressure = 100 kPa, R=8.3 J/mol. K) (Neglect mass of the piston)

1. 24.8
2. 10.96
3. 15.04
4. 29.98

Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume Vfinal=27V is J.

1. -2PV (3 3-1 )
2. 43PV
3. - 43PV
4. 34PV

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same P, V, T. Heating is started from left side until pressure changes to 27P8. If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is litres. (for this ideal gas CP/CV=1.5)

1. 3
2. 4
3. 14
4. 9

Consider the following statements: Choose the correct combination of statements from the options given below:

1. C, D and E Only
2. A, B and C Only
3. A, B and D Only
4. B, C and D Only

An ideal gas undergoes a process maintaining relation between pressure (P) and volume (V) as P=P0 (1+ ( V0V )2 )-1, where P0 and V0 are constants. If two samples A and B (two moles each) with initial volumes V0 and 3V0 respectively undergo above mentioned process and attain same pressure, then the difference in the temperatures of these samples, TB-TA is . (R = gas constant)

1. 9P0V08R
2. 11P0V010R
3. 7P0V06R
4. 13P0V011R

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of Q : U : W is .

1. 2 : 3 : 5
2. 5 : 3 : 2
3. 2 : 5 : 7
4. 7 : 5 : 2

In the following p - V diagram the equation of state along the curved path is given by (V - 2)2 = 4ap where a is a constant. The total work done in the closed path is [figure]

1. + 13a
2. - 1a
3. 12a
4. - 13a

Densities of water at 4 and 20 are 1000 kg/m3 and 998 kg/m3 respectively. The increase in internal energy of 4 kg of water when it is heated from 4 to 20 is J. (specific heat capacity of water = 4.2 kJ/kg K and 1 atmospheric pressure = 105 Pa)

1. 268799.2
2. 315826.2
3. 234699.2
4. 258700.8

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P1 to P2 is Joule (P1 = 21.7 Pa and P2 = 30 Pa, Cv = 21 J/K mol, R = 8.3 J/mol K). The value of is . [figure]

1. 21
2. 28
3. 24
4. 15

One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature 27 and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from 27 doing the same amount of work W, then its final temperature will be (close to) . ( e 2 = 0.693)

1. -56
2. -117
3. -30
4. -189

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of 17 cm2 and fitted with a light movable frictionless piston. The gas is heated slowly by supplying 126 J heat. If the temperature rises by 4 , then the piston will move cm. (atmospheric pressure = 105 Pa)

1. 1.55
2. 14.5
3. 15.5
4. 1.45

The volume of an ideal gas increases 8 times and temperature becomes (1/4)th of initial temperature during a reversible change. If there is no exchange of heat in this process ( Q = 0) then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :

1. NH3
2. O2
3. CO2
4. He

A monoatomic gas having = 53 is stored in a thermally insulated container and the gas is suddenly compressed to ( 18 )th of its initial volume. The ratio of final pressure and initial pressure is: ( is the ratio of specific heats of the gas at constant pressure and at constant volume)

1. 16
2. 32
3. 28
4. 40

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 cm3 and temperature 27 . The change in temperature when the gas is adiabatically compressed to 200 cm3 is: (Take = 1.5; is the ratio of specific heats at constant pressure and at constant volume)

1. 300 K
2. 600 K
3. 327 K
4. 522 K

During the melting of a slab of ice at 273 K at atmospheric pressure :

1. Internal energy of ice-water system remains unchanged.
2. Positive work is done by the ice-water system on the atmosphere.
3. Positive work is done on the ice-water system by the atmosphere.
4. Internal energy of the ice-water system decreases.

[figure] A piston of mass M is hung from a massless spring whose restoring force law goes as F = -kx3, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with 'n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height L0 to L1, the total energy delivered by the filament is: (Assume spring to be in its natural length before heating)

1. nRT ( L1L0 ) + Mg(L1 - L0) + 3k4 (L14 - L04 )
2. nRT ( L1L0 ) + Mg(L1 - L0) + k4 (L14 - L04 )
3. nRT ( L12L02 ) + Mg2(L1 - L0) + k4 (L14 - L04 )
4. 3nRT ( L1L0 ) + 2Mg(L1 - L0) + k3 (L13 - L03 )

An ideal gas exists in a state with pressure P0, volume V0. It is isothermally expanded to 4 times of its initial volume (V0), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

1. P0V0( 2 - 0.75)
2. P0V0(2 2 - 0.75)
3. P0V0(2 2 - 0.25)
4. P0V0( 2 - 0.25)

In an adiabatic process, which of the following statements is true?

1. The internal energy of the gas decreases as the temperature increases
2. The molar heat capacity is zero
3. Work done by the gas equals the increase in internal energy
4. The molar heat capacity is infinite

Identify the characteristics of an adiabatic process in a monoatomic gas. Choose the correct answer from the options given below :

1. (B), (D) only
2. (B), (E) only
3. (A), (C), (E) only
4. (A), (C), (D) only

The work done in an adiabatic change in an ideal gas depends upon only :

1. change in its pressure
2. change in its temperature
3. change in its specific heat
4. change in its volume

A Carnot engine (E) is working between two temperatures 473 K and 273 K. In a new system two engines - engine E1 works between 473 K to 373 K and engine E2 works between 373 K to 273 K. If 12, 1 and 2 are the efficiencies of the engines E, E1 and E2, respectively, then

1. 12 = 1 2
2. 12 = 1 + 2
3. 12 1 + 2
4. 12 < 1 + 2