Question

The reversible expansion ob an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

• A. $T_1 = T_2$
• B. $T_3 > T_1$
• C. $w_{isothermal} > w_{adiabatic}$
• D. $?U_{isothcrmal} > ?U_{adiabatic}$

Answer 1

Answer: (D)

$?U_{isothcrmal} > ?U_{adiabatic}$

Answer 2

(a) Since, change of state $(p_1, V_1 , T_1) \, to \, (p_2, V_2, T_2)$ is isothermal therefore, $T_3 < T_2$. (b) Since, change of state $(p_1, V_1 , T_1,) \, to \, (p_3, V_3, T_3)$ is an adiabatic expansion it brings about cooling of gas, therefore, $T_3 < T_1$ (c) Work done is the area under the curve of p-V diagram. As obvious from the given diagram, magnitude of area under the isothermal curve is greater than the same under adiabatic curve, hence $W_{isothermal} > W_{adiabatic}$ (d) $?U = nC_u?T$ In isothermal process, $?U = 0 \, as \, ?T = 0$ In adiabatic process. $?U = nC_p,(T_3 - T_1 ) < 0 \, as \, T_3 < T_1$. $\Rightarrow \, \, \, \, \, ?U_{isotherml} > ?U_{adiabatic}$ NOTE Here only magnitudes of work is being considered otherwise both works have negative sign.