Match the following List - I amp; List - II i) Isothermal process...

Work done in any quasi-static process (=W=\int_{V_1}^{V_2} P d V). Evaluate this for each process. i) Isothermal process (($\mathrm{T}=$ constant). Use ideal gas: $P V=n R T$ (constant (T \Rightarrow n R T=) constant). (W=\int_{V_1}^{V_2} P d V=\int_{V_1}^{V_2} $\frac{n R T}{V}$d V=n R T \ln $\frac{V_2}{V_1}$ So isothermal (\Rightarrow) match (c). ii) Isobaric process (($\mathrm{P}=$ constant). If pressure is constant, (W=\int_{V_1}^{V_2} P d V=P$\left(V_2-V_1\right)) So isobaric (\Rightarrow) match (d). iii) Isochoric process (($\mathrm{V}=$constant). If volume is constant$d V=0$, therefore (W=\int_{V_1}^{V_2} P d V=0) So isochoric (\Rightarrow) match (a). iv) Adiabatic (reversible) process.$ For adiabatic reversible: (P V^\gamma=constant. Let (P V^\gamma=$K). Then (W=\int_{V_1}^{V_2} P d V=K \int_{V_1}^{V_2} V^{-\gamma} d V=$\frac{K}{1-\gamma}\left(V_2^{1-$\gamma$}-V_1^{1-$\gamma$}\right)) Using (K=P_1 V_1^$\gamma=$P_2 V_2^$\gamma$ and simplifying gives the standard form (W=$\frac{P_1 V_1-P_2 V_2}{\gamma-1} .$ So adiabatic (\Rightarrow) match (b). Final matching: i - c, ii $-d$, iii $-a$, iv $-b$.