According to first law of thermodynamics

$\Delta \text{Q}=\Delta \text{U}+\Delta \text{W}$

For an adiabatic process, $\Delta \text{Q=0}$

$\therefore$  $0=\Delta \text{U}+\Delta \text{W}$

or  $\Delta \text{U}=-\Delta \text{W}$

or  $\mathrm{n}{\text{C}}_{\text{V}}\Delta \text{T}=-\Delta \text{W}$

or  ${\text{C}}_{\text{V}}=\frac{-\Delta \text{W}}{\mathrm{n}\Delta \text{T}}=\frac{-\left(-\text{146}\right)\times {\text{10}}^3}{\left(1\times {\text{10}}^3\right)\times 7}$

${\mathrm{C}}_{\mathrm{v}}=20.8 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$

For diatomic gas,

${\text{C}}_{\text{V}}=\frac{5}{2}\text{R}=\frac{5}{2}\times {\text{8.3 = 20.8 J mol}}^{-1}{\text{ K}}^{-1}$

Hence the gas is diatomic.