If $\gamma$ denotes the ratio of two specific heats of a gas, the ratio of the slopes of adiabatic and isothermal $PV$ curves at their point of intersection is:

$Assertion:$ In adiabatic compression,the internal energy and temperature of the system decrease.
$Reason:$ Adiabatic compression is a slow process.

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

$A$ hypothetical gas expands adiabatically such that its volume changes from $8 \ L$ to $27 \ L$. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$, then the ratio of $\frac{C_P}{C_V}$ will be:

Assertion $(A)$: When an ideal gas is compressed adiabatically,its temperature and the average kinetic energy of the gas molecules increase.
Reason $(R)$: The kinetic energy increases because of collisions of molecules with the moving parts of the wall.

The work done in which of the following processes is equal to the internal energy of the system?