The work of $$146 kJ$$  is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $${7^ \circ }C.$$ The gas is $$\left( {R = 8.3\,\,J\,mo{l^{ - 1}}{K^{ - 1}}} \right)$$

Solution :
$$\eqalign{ & W = \frac{{nR\Delta T}}{{1 - \gamma }} \cr & \Rightarrow \,\, - 146000 = \frac{{1000 \times 8.3 \times 7}}{{1 - \gamma }} \cr & {\text{or }}1 - \gamma = - \frac{{58.1}}{{146}} \cr & \Rightarrow \,\,\gamma = 1 + \frac{{58.1}}{{146}} \cr & = 1.4 \cr} $$
Hence the gas is diatomic.