Question

Six grams of hydrogen gas at a temperature of $273K$ was isothermally expanded to five times its initial volume and then isochorically heated so that the pressure in the final state becomes equal to that in the initial state. Find the total amount of heat absorbed by the gas during the entire process (in joules).

• A. $78919.4$
• B. $78990.2$
• C. $80281.6$
• D. $80110.8$

Answer 1

The correct option is A $78919.4$

The processes represent on the pressure-volume diagram by the curve 1 to 2 (isothermal) and the line 2 to 3 (isochoric). Here $P_1=P_3$
For the process 1 to 2 (isothermal)
$T_2=T_1$, $V_2=5V_1$
$\Delta H=\Delta U+W=0+W$
$⟹\Delta H=2.303nR{T}_1\log \frac{V_2}{V_1}$
$\Delta H=2.303\times \left(\frac{6}{2}\right)\times 8.3\times 273\times \log 5=10942.4J$
State 1 and State 3 are at the same pressure.
$⟹\frac{V_1}{T_1}=\frac{V_3}{T_3}⟹T_3=\frac{V_3}{V_1}{T}_1=5\times 273=1365K$
Process 2 to 3: $\Delta H=\Delta U+W$
$⟹\Delta H=n{C}_v\Delta T+0$
$\Delta H=\frac{6}{2}\times \frac{5}{2}R\times (T_3-T_2)$
$⟹\Delta H=7.5\times 8.3\times (1365-273)J=67977J$
Thus total heat absorbed$=\Delta H_{1\to 2}+\Delta H_{2\to 3}=78919.4J$