T₁ = 273 + 27 = 300K

T₂ = 273 + 927 = 1200K

For adiabatic process,

${P^{1 - \gamma }}{T^\gamma }$ = constant

$\Rightarrow {P_1}^{1 - \gamma }{T_1}^\gamma = {P_2}^{1 - \gamma }{T_2}^\gamma$

$\Rightarrow {\left( {{{{P_2}} \over {{P_1}}}} \right)^{1 - \gamma }} = {\left( {{{{T_1}} \over {{T_2}}}} \right)^\gamma }$

$\Rightarrow {\left( {{{{P_1}} \over {{T_2}}}} \right)^{1 - \gamma }} = {\left( {{{{T_2}} \over {{T_1}}}} \right)^\gamma }$

${\left( {{{{P_1}} \over {{P_2}}}} \right)^{1 - 1.4}} = {\left( {{{1200} \over {300}}} \right)^{1.4}}$

${\left( {{{{P_1}} \over {{P_2}}}} \right)^{ - 0.4}} = {\left( 4 \right)^{1.4}}$

${\left( {{{{P_2}} \over {{P_1}}}} \right)^{0.4}} = {4^{1.4}}$

${P_2} = {P_1}{4^{\left( {{{1.4} \over {0.4}}} \right)}} = {P_1}{4^{\left( {{7 \over 2}} \right)}}$

= P₁ (2⁷) = 2 × 128 = 256 atm