For an adiabatic process,if $\gamma = 2.5$ and the volume becomes $1/8$ of its initial volume,then the new pressure $P'$ is (initial pressure $= P$):

In a process, the work done by the system is equal to the decrease in its internal energy. The process that the system undergoes is

Work done on heating one mole of monoatomic gas adiabatically through $20^{\circ} C$ is $W$. Then, the work done on heating $6$ moles of rigid diatomic gas through the same change in temperature is: (in $W$)

The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be (Given $\gamma =$ ratio of specific heats at constant pressure and at constant volume).

In which of the following processes,heat is neither absorbed nor released by a system?

$A$ monoatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume is $TV^{x} = \text{constant}$, then $x$ is