JEE Main 2007 — Thermodynamics

If $\mathrm{C}_p$ and $\mathrm{C}_{\mathrm{v}}$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of lengths $\ell_1$ and $\ell_2$ and thermal conductivities $k_1$ and $k_2$ respectively. The temperature at the interface of the two sections is 

When a system is taken from state $i$ to state $f$ along the path $\mathrm{iaf}$, it is found that $Q=50 \mathrm{~cal}$ and $\mathrm{W}=20 \mathrm{~cal}$. Along the path' $\mathrm{ibf}$ $\mathrm{Q=36 ~cal}$. $\mathrm{W}$ along the path $\mathrm{ibf}$ is