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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Match List-$I$ with List-$II$ :
List-$I$List-$II$
$A$. Isothermal Process$I$. Work done by the gas decreases internal energy
$B$. Adiabatic Process$II$. No change in internal energy
$C$. Isochoric Process$III$. The heat absorbed goes partly to increase internal energy and partly to do work
$D$. Isobaric Process$IV$. No work is done on or by the gas

Choose the correct answer from the options given below :

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