An adiabatic process occurs at constant

An ideal gas undergoes an adiabatic process from state $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$. The work done during the process is ..... (where $\mu$ = number of moles,$C_P$ and $C_V$ = molar specific heats).

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 $W$)

One mole of an ideal gas $\left(\gamma = \frac{5}{3}\right)$ at $127^{\circ} C$ is compressed adiabatically to $\left(\frac{8}{27}\right)$ of its initial volume. Find the magnitude of the work done on the system in $cal$.

$A$ mass of diatomic gas $(\gamma = 1.4)$ at a pressure of $2 \text{ atm}$ is compressed adiabatically so that its temperature rises from $27^{\circ}C$ to $927^{\circ}C$. The pressure of the gas in the final state is ...... $\text{atm}$.

$A$ gas does $4.5 \,J$ of external work during adiabatic expansion. If its temperature falls by $2 \,K$, then its internal energy will be