Thermodynamics (Physics)

[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

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below:

1. (A) is true but (R) is false
2. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
3. (A) is false but (R) is true
4. Both (A) and (R) are true and (R) is the correct explanation of (A)

A poly-atomic molecule (CV=3R, CP=4R, where R is gas constant) goes from phase space point A ( PA=105 Pa, VA=4 10-6 m3 ) to point B ( PB=5 104 Pa, VB=6 10-6 m3 ) to point C ( PC=104 Pa, VC=8 10-6 m3 ). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is : [figure]

1. 500R( 3+ 4)
2. 450R( 4- 3)
3. 500R 2
4. 400R 4

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

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. Choose the correct answer from the options given below:

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

The temperature of 1 mole of an ideal monoatomic gas is increased by 50 at constant pressure. The total heat added and change in internal energy are E1 and E2, respectively. If E1E2= x9 then the value of x is .