Thermodynamic Potential MSQ - IIT JAM MCQ

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

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

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.

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: 

From second law of thermodynamics

and dQ = dU + pdV

⇒ TdS = dU + pdV
⇒ dU = TdS – pdV

and 
The correct answers are: 

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.

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  

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:
 

Since      F = U – TS
dF = TdS – pdU – TdS – SdT
keeping V constant

Also, dU = TdS – pdV

The correct answers are:

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