Solution:

Since when $$n = \pm \infty $$   the equation $$P{V^n} = {\text{constant}}$$     is leading to volume $$=$$ constant the process is called as isochoric process on multiplying the power with $$\frac{1}{\infty }$$ we get the equation $$v = {\text{constant}}.$$

Solution:

An adiabatic process is represented by $$p{v^\gamma } = {\text{constant}}$$    now by replacing the $$p$$ with $$\frac{{nRT}}{v}$$  we get $$T{V^{\gamma - 1}} = {\text{constant}}$$    and by replacing the $$V$$ with $$\frac{{nRT}}{P}$$  we get the equation $${P^{1 - \gamma }}{T^\gamma } = {\text{constant}}.$$

Solution:

A reversible process is such a process where the system and surroundings must be brought to the initial positions when the system is brought to initial position for that to achieve the system should not contain friction.

Solution:

Clausius–Clapeyron equation is used during the phase change process and since the melting is a phase change process we can use it during the melting.

Solution:

The kinetic energy of the molecules is Zero at absolute zero temperature (0K) as all the molecules will be at rest at this temperature.

Solution:

We know the concept of fugacity is originated from the equation $$d{\mu _i} = pdv - sdT$$    for an pure gas.
Under constant temperature and assuming an ideal gas we can write this as $$d\mu = RTdlnP$$    and for an real gas the same equation is assumed keeping all the non-ideality in the term fugacity and written as $$d\mu = RTdlnf$$
So, we can say for an ideal gas $$f = p.$$

Solution:

Lenz’s law is derived from law of conservation of energy.