Question

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

$AB⟶$ Isothermal expansion
$AC⟶$ 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.