One mole of an ideal gas undergoes the following cyclic process:<br>(i) Isochoric heating from () to — Thermodynamics and Thermochemistry Chemistry Question
Question
One mole of an ideal gas undergoes the following cyclic process:<br>(i) Isochoric heating from ($P_1, V_1, T_1$) to double temperature.<br>(ii) Isobaric expansion to double volume.<br>(iii) Linear expansion (on $P-V$ curve) to ($P_1, 8V_1$).<br>(iv) Isobaric compression to initial state.<br>If $T_1 = 300\text{ K}$, the magnitude of net work done by the gas in the cyclic process is
💡 Solution & Explanation
The process forms a closed loop in a P-V diagram. Area enclosed is the net work. Process 1$\to$2 (isochoric to $2T_1$) creates state $(V_1, 2P_1)$. Process 2$\to$3 (isobaric to $2V_1$) creates state $(2V_1, 2P_1)$. Process 3$\to$4 (linear to $P_1, 8V_1$). Process 4$\to$1 (isobaric to $V_1, P_1$). The enclosed area is a rectangle ($V_1$ to $2V_1$, $P_1$ to $2P_1$) of area $1 P_1V_1$ plus a triangle ($2V_1$ to $8V_1$, height $P_1$) of area $0.5 \times 6V_1 \times P_1 = 3 P_1V_1$. Total Area $= 4 P_1V_1 = 4 RT_1 = 4 \times 2 \text{ cal/K} \times 300 \text{ K} = 2400 \text{ cal}$.