A gas may expand either adiabatically or isothermally. A number of $P-V$ curves are drawn for the two processes over different range of pressure and volume. It will be found that

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)

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):

An ideal gas at ${27^o}C$ is compressed adiabatically to $\frac{8}{{27}}$ of its original volume. If $\gamma = \frac{5}{3}$, then the rise in temperature is........ $K$

A certain mass of gas at $273 K$ is expanded to $81$ times its volume under adiabatic condition. If $\gamma = 1.25$ for the gas, then its final temperature is ..... $^oC$

Which one is the correct option for the two different thermodynamic processes ?