A mass of diatomic gas ($\mathrm{\gamma } = 1.4$) at a pressure of 2 atm is compressed adiabatically so that its temperature rise from ${27}^0\mathrm{C} \mathrm{to} {927}^0\mathrm{C}.$ The pressure of the gas is final state is

${\mathrm{T}}_1 = 273 + 27 = 300 \mathrm{K}$

${\mathrm{T}}_2 = 273 + 927 = 1200 \mathrm{K}$

Gas equation for adiabatic process ${\mathrm{pV}}^{\mathrm{\gamma }} = \mathrm{constant}$

$\mathrm{p}{\left(\frac{\mathrm{T}}{\mathrm{p}}\right)}^{\mathrm{\gamma }} = \mathrm{constant} (\therefore \mathrm{pV} = \mathrm{RT})$

$\frac{{\mathrm{p}}_2}{{\mathrm{p}}_1} = {\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)}^{\frac{\mathrm{\gamma }}{\mathrm{\gamma }-1}} \mathrm{or} {\mathrm{p}}_2 = {\mathrm{p}}_1{\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)}^{\frac{\mathrm{\gamma }}{\mathrm{\gamma }-1}}$

${\mathrm{p}}_2 = 2{\left(\frac{1200}{300}\right)}^{\frac{1.4}{1.4-1}}$

${\mathrm{p}}_2 = 256 \mathrm{atm}.$