We know that for an adiabatic process $p{V}^N=$a constant. Evaluate "a constant" for an adiabatic process involving exactly $3\mathrm{.}1$ mol of an ideal gas passing through the state having exactly $p=1\mathrm{.}5$atm and $T=278K.$ Assume a diatomic gas whose molecules have rotation but not oscillation. Use the SI units for the given quantities but omit unit for the final result.