A thermodynamic process of one mole ideal monoatomic gas is shown in figure. The efficiency of cyclic process $ABCA$ will be:

One mole of a gas is subjected to two process $AB$ and $BC$ one after the other as shown in the figure. $BC$ is represented by, $P{V}^{\mathrm{n}}=\text{constant}$. We can conclude that (where, $T=$temperature, $W=$work done by gas, $V=$volume and $U=$internal energy),

An ideal gas is taken from state $1$ to state $2$ through optional path $A, B, C$ and $D$, as shown in the $PV$ diagram. Let $Q, W$ and $U$ represent the heat supplied, work done and change in internal energy of the gas, respectively. Then,

One mole of an ideal gas requires $207 \mathrm{J}$ heat to raise the temperature by $10 \mathrm{K}$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by $10 \mathrm{K}$ then heat required is [given gas constant $R=8.3 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$.]

Assertion: Equal volumes of monatomic and polyatomic gases are adiabatically compressed separately to equal compression ratio $\frac{P_2}{P_1}$. Then polyatomic gas will have greater final volume.

Reason: Among ideal gases, molecules of a monatomic gas have the smallest number of degrees of freedom.

Two samples $1$ and $2$ are initially kept in the same state. Sample $1$ is expanded through an isothermal process whereas sample $2$ through an adiabatic process up to the same final volume. Let $P_1$ and $P_2$ be the final pressures of the samples $1$ and $2$, respectively, then,