Two systems have thermodynamic probabilities of 3.0 10²⁷ and 1.8 1028 respectively. Calculate the entropies of the individual systems and as well as their composite system and verify the Boltzmann relation.

Using Maxwell’s relations, deduce first and second energy equations.

Derive the single-particle partition function for an ideal monatomic gas consisting of N identical particles occupying a volume V. Obtain expressions for the entropy and pressure of this system.

Write an expression of Planck’s law of black body radiation and hence obtain Stefan’s-Boltzmann law.

The number density of copper atoms is 8.4910²⁸ atoms m^–3 . If each atom contributes one free electron for conduction, examine whether the electron gas is strongly degenerate at room temperature.

Consider a thermodynamic system consisting of 3 mol of an ideal gas occupying 0.03 m³ volume at 300 K temperature. Determine its initial pressure. For this gas, γ=1.4. It undergoes the following processes:

i) It is compressed to 0.01 m³ volume isothermally. Determine the pressure of the gas.

ii) then it is allowed to expand adiabatically, till it attains 1 atm pressure. Determine the final volume. (1 atm = 101325 Nm^-2 )

Draw a labeled indicator diagram of these processes.

What do you understand by intensive and extensive variables of a system? State with reasons, which of the following variables are intensive and which are extensive?

i) Number of gas molecules enclosed in a box;

ii) Density of gas in a box;

iii) Wavelength of radiation emitted by a black body at temperature T;

iv) Intensity of radiation emitted by a black body at temperature T.