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*Multiple options can be correct

QUESTION: 1

The total internal energy of the system is given by

Solution:

U = Nɛ where N is the total number of molecules in the system and ɛ represents the energy of one molecule.

*Multiple options can be correct

QUESTION: 2

For liquifying gas, it is essential that the gas

Select one or more:

Solution:

Processes like Linde’s process for air liquefaction need a positive Joule Thomson coefficient, hence we can only operate at temperature below the inversion temperature. Similarly, we know that above the critical temperature, gas cannot be liquified by varying the pressure, therefore the temperature of the gas should be below critical temperature.

The correct answers are: Should be below its temperature of inversion, Should be below the critical temperature

*Multiple options can be correct

QUESTION: 3

Potential energy of a substance is a function of only

Solution:

Potential energy is defined as stored energy or mechanical energy. It depends only on the strength of gravitational field, its mass & its height relative to same reference point. Therefore it is not dependent on any of the velocity, pressure & temperature.

*Multiple options can be correct

QUESTION: 4

Which among the following for Maxwell’s relation are correct?

(U - internal energy, H - enthalpy, S - entropy)

Select one or more:

Solution:

We know that H = U + pV

⇒ dH = dV + pdV + Vdp

and dV = TdS + VdP

⇒ dH = TdS + Vdp

Now keeping p as constant,

keeping S as constant,

The correct answers are:

*Multiple options can be correct

QUESTION: 5

According to consequences of the second law of thermodynamics (symbols have their usual meaning)

Select one or more:

Solution:

From second law of thermodynamics

and dQ = dU + pdV

⇒ TdS = dU + pdV

⇒ dU = TdS – pdV

and

The correct answers are:

*Multiple options can be correct

QUESTION: 6

Which of the following statements are true?

Select one or more:

Solution:

A massive ideal gas with only one type of particle is uniquely described by three state functions such as temperature, volume and number of particles. However for a black body, the energy distribution is established by interaction of photons with matter, usually walls of container. In this interaction, number of photons is not conserved. As a result, chemical potential is zero.

Further (b) and (c) are basic facts about the chemical potential and hence are true.

The correct answers are: Chemical potential for photon is zero, In phase equilibrium, total sum of chemical potentials is zero, Chemical potential of electron at zero Kelvin is same as Fermi Energy.

*Multiple options can be correct

QUESTION: 7

Denoting temperature, entropy and internal energy by T, S and U respectively and their initial and final values by subscript i and f respectively, the Joule Thomson expansion of an ideal gas can be expressed as

Select one or more:

Solution:

In Joule-Thomson expansion of an ideal gas, internal energy and temperature remains same but entropy increases hence (a), (c) and (d) are correct options.

The correct answers are

*Multiple options can be correct

QUESTION: 8

Which of the following are correct terms of Maxwell’s relation

Select one or more:

Solution:

Except option (c), all the other options give one of Maxwell’s equation and the fourth missing equal is given as

The correct answers are:

*Multiple options can be correct

QUESTION: 9

For an isolated thermodynamical system p, V, T, U, S and F represent the pressure, volume, temperature, internal energy,entropy and free energy respectively. Then, following relation are true

Select one or more:

Solution:

Since F = U – TS

dF = TdS – pdU – TdS – SdT

keeping V constant

Also, dU = TdS – pdV

The correct answers are:

*Multiple options can be correct

QUESTION: 10

For a thermodynamic system Helmholtz free energy is a function of

Select one or more:

Solution:

F = U – TS

⇒ dF = dU – TdS – SdT

dF = TdS – pdV – TdS – SdT

⇒ dF = –pdV – SdT

⇒ F is a function of V and T.

The correct answers are:

T,V

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