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 $:$

  • A
    Both $(A)$ and $(R)$ are true but $(R)$ is $\text{NOT}$ the correct explanation of $(A)$.
  • B
    $(A)$ is true but $(R)$ is false.
  • C
    Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.
  • D
    $(A)$ is false but $(R)$ is true.

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In Column $-I$ processes and in Column $-II$ formulas of work are given. Match them appropriately:
Column $-I$ Column $-II$
$(a)$ Isothermal process $(i)$ $W = \frac{\mu R(T_1 - T_2)}{\gamma - 1}$
$(b)$ Adiabatic process $(ii)$ $W = P\Delta V$
$(iii)$ $W = 2.303\mu RT \log_{10} \left( \frac{V_2}{V_1} \right)$

The specific heat of hydrogen gas at constant pressure is $C_P = 3.4 \times 10^3 \text{ cal/kg } ^oC$ and at constant volume is $C_V = 2.4 \times 10^3 \text{ cal/kg } ^oC$. If $1 \text{ kg}$ of hydrogen gas is heated from $10^oC$ to $20^oC$ at constant pressure,the external work done by the gas is:

One mole of an ideal gas having initial volume $V$,pressure $2P$ and temperature $T$ undergoes a cyclic process $ABCDA$ as shown below. The net work done in the complete cycle is:

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Two identical samples of a gas are allowed to expand $(i)$ isothermally and $(ii)$ adiabatically. The work done is:

Two moles of a gas are expanded to double their volume by two different processes. One is isobaric and the other is isothermal. If $W_1$ and $W_2$ are the works done, respectively, then:

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