\(\frac{{{T^\gamma }}}{{{P^{\gamma  - 1}}}} = constant\)

\(\therefore \,{\left( {\frac{{{T_i}}}{{{T_f}}}} \right)^\gamma } = {\left( {\frac{{{p_i}}}{{{p_f}}}} \right)^{\gamma  - 1}}\,\,;\,\,{p_f} = {p_i}{\left( {\frac{{{T_f}}}{{{T_i}}}} \right)^{\frac{\gamma }{{\gamma  - 1}}}}\)                \(...(i)\) 

\(Here,\,{T_i} = {27^ \circ }C = 300\,K,\,{T_f} = {927^ \circ }C = 1200\,k\)

\({p_i} = 2\,atm,\,\gamma  = 1.4\)

Substituting these values in eqn \((i)\), we get

\({P_f} = \left( 2 \right){\left( {\frac{{1200}}{{300}}} \right)^{\frac{{1.4}}{{1.4 - 1}}}}\)

\( = \left( 2 \right){\left( 4 \right)^{1.4/0.4}} = 2{\left( {{2^2}} \right)^{7/2}} = \left( 2 \right){\left( 2 \right)^7} = {2^8} = 256\,atm\)