If system $A$ is in thermal equilibrium with $B$ and $B$ is separately in thermal equilibrium with $C,$ then $A$ and $C$ are in thermal equilibrium. From which thermodynamics law, does this follow?

If ideal diatomic gas follows the process as shown in graph where $T$ is temperature in $\mathrm{kelvin}$ and $V$ is volume $\left({\mathrm{m}}^3\right)$, then molar heat capacity for this process will be [in terms of gas constant $R$],

A thermodynamic system is taken through the cycle $ABCD$ as shown in the figure. Heat rejected by the gas during the cycle is:

Helium gas goes through a cycle $\mathrm{ABCDA}$ (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly (Assume the gas to be close to ideal gas) 

A Carnot engine takes $3\times {10}^6 \mathrm{cal}$ of heat from a reservoir at $627 °\mathrm{C}$ and gives it to a sink at $27 °\mathrm{C}$. The work done by the engine is,