Figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part containing identical gas at pressure $P_0$ . Initially temperature of left and right part is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep the piston at rest. Find the value of external force required when thermal equilibrium is reached. ( $A =$ Area of piston)

A van der Waal's gas obeys the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$. Its internal energy is given by $U=C T-\frac{n^2 a}{V}$. The equation of a quasistatic adiabat for this gas is given by

In thermodynamic processes which of the following statements is not true?

Check the statement are trrue or false :

$1.$ For an adiabatic process $T{V^{\gamma  - 1}}$ $=$ constant.

$2.$ Charging process of battery is a reversible process.

$3.$ Water falls below from height is a reversible process.

$4.$ Internal energy, volume and mass are intensive variable while pressure, temperature and density are extensive variables.

A gas is being compressed adiabatically. The specific heat of the gas during compression is

At $N.T.P.$ one mole of diatomic gas is compressed adiabatically to half of its volume $\gamma = 1.41$. The work done on gas will be ....... $J$