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, $\mathrm{PV}=$ constant, while in adiabatic process $\mathrm{PV}^\gamma=$ 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 :

• Correct answer
  A

  Both (A) and (R) are true and (R) is the correct explanation of (A)
• B

  Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
• C

  (A) is true but (R) is false
• D

  (A) is false but (R) is true

Solution

$\left(\frac{\mathrm{dP}}{\mathrm{dV}}\right)_{\text {Adiabatic }}>\left(\frac{\mathrm{dP}}{\mathrm{dV}}\right)_{\text {Isothermal }}$

Hence, the correct answer is option: 'A'.