Q49 / 180 · NEET 2019 (Odisha) · Chemistry

Reversible expansion of an ideal gas under isothermal and adiabatic conditions are as shown in the figure. Figure
$A B \rightarrow$ Isothermal expansion $A C \rightarrow$ 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
    $W_{\text {isothermal }}>W_{\text {adiabatic }}$
  • Correct answer
    D
    $T_c>T_A$

Solution

From first law of thermodynamics, $$ \Delta \mathrm{U}=\mathrm{q}+\mathrm{W} $$ In adiabatic expansion, $q=0$ $$ \therefore \quad \Delta \mathrm{U}=\mathrm{W} $$ During expansion of a gas $w$ is negative i.e $w < 0$ or $\Delta \mathrm{U} < 0$. We know that, $\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $$ \begin{array}{lclc} \therefore & \mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T} < 0 & \text { or } & \Delta \mathrm{T} < 0 \\ \therefore & \mathrm{T}_{\mathrm{C}}-\mathrm{T}_{\mathrm{A}} < 0 & \text { or } & \mathrm{T}_{\mathrm{C}} < \mathrm{T}_{\mathrm{A}} \end{array} $$ Thus, option (4) is incorrect while the remaining options are correct.

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

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