Question

Reversible expansion of an ideal gas under isothermal and adiabatic conditions are as shown in the figure.

$A B \longrightarrow$ Isothermal expansion
$A C \longrightarrow$ Adiabatic expansion
Which of the following option is not correct?

• A. $\Delta S_{\text {isothermal }} > \Delta S_{\text {adiabatic }}$
• B. $T_{A}=T_{B}$
• C. $W_{\text {isothermal }} > W_{\text {adiabatic }}$
• D. $T_{C} > T_{A}$

Answer 1

Answer: (D)

Option (d) is incorrect. It's correct form is as follows:
From first law of thermodynamics,
$\Delta U=q+ W$
In adiabatic expansion, $q=0$
$\therefore \Delta U=W$
During expansion of a gas, $W$ is negative,
i.e $W<0$ or $\Delta U<0$.
We know that, $\Delta U=n C_{V} \Delta T$
$\therefore n C_{V} \Delta T< 0$ or $\Delta T< 0$
$\therefore T_{C}-T_{A} < 0$ or $T_{C} < T_{A}$
Rest other options are correct.