Write the equation for the work done during the compression of an ideal gas.

For a monoatomic gas, the work done at constant pressure is $W$. The heat supplied at constant volume for the same rise in temperature of the gas is

$A$ gas of mass '$m$' and molecular weight '$M$' is flowing in an insulated tube with a velocity '$2V$'. If the flow of the gas is suddenly stopped and all the kinetic energy is utilized to compress the gas,the increase in the temperature of the gas is ($\gamma$ is the ratio of specific heats,$R$ is the universal gas constant).

An ideal monoatomic gas is carried along the cycle $ABCDA$ as shown in the figure. The total heat absorbed during this process is (in $p_0 V_0$)

$P-V$ diagram of a cyclic process $ABCA$ is as shown in figure. Choose the correct statement.

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ With the increase in the pressure of an ideal gas,the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason $(R) :$ In isothermal process,$PV =$ constant,while in adiabatic process $PV^\gamma =$ constant. Here $\gamma$ is the ratio of specific heats,$P$ is the pressure and $V$ is the volume of the ideal gas. In the light of the above statements,choose the correct answer from the options given below $:$