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.

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.

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

Derive an expression for efficiency of a Carnot engine using T-S diagram. A Carnot engine has an efficiency of 50 percent when its sink temperature is at 27 ºC. Calculate the change in source temperature for increasing its efficiency to 60 percent.

Define viscosity. Discuss the effect of temperature and pressure on viscosity.

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.

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