Ideal gas obey's all charle's laws and boyle's law.

Therefore

\(\displaystyle{P}_{{1}}\cdot{V}_{{1}}={P}_{{2}}\cdot{V}_{{2}}\)

and

\(\displaystyle{\frac{{{V}_{{1}}}}{{{T}_{{1}}}}}={\frac{{{V}_{{2}}}}{{{T}_{{2}}}}}\)

Volume of the gas at \(\displaystyle{220}^{\circ}\)

\(\displaystyle{V}_{{2}}={\frac{{{V}_{{1}}}}{{{T}_{{1}}}}}\times{T}_{{2}}={\frac{{{5}}}{{{293}}}}\times{493}={8.41}\)

(b)The pressure of the gas at P\(\displaystyle{220}^{\circ}{C}\)

\(\displaystyle{P}_{{2}}={\frac{{{P}_{{1}}{V}_{{1}}}}{{{V}_{{2}}}}}={\frac{{{1}\times{5}}}{{{8.41}}}}={0.59}\)

Force acting on the piston

\(\displaystyle{F}={P}\times{A}={0.59}\times{101.325}\times{10}^{{3}}\times{0.01}\)

\(\displaystyle={597.81}\) N

Displacement of the piston

\(\displaystyle{x}={\frac{{\text{Force}}}{{\text{force constant}}}}={\frac{{{F}}}{{{K}}}}={\frac{{{597.81}}}{{{2.00}\times{10}^{{3}}}}}={0.293}\)

\(\displaystyle{m}={29.3}{c}{m}\)

Therefore

\(\displaystyle{P}_{{1}}\cdot{V}_{{1}}={P}_{{2}}\cdot{V}_{{2}}\)

and

\(\displaystyle{\frac{{{V}_{{1}}}}{{{T}_{{1}}}}}={\frac{{{V}_{{2}}}}{{{T}_{{2}}}}}\)

Volume of the gas at \(\displaystyle{220}^{\circ}\)

\(\displaystyle{V}_{{2}}={\frac{{{V}_{{1}}}}{{{T}_{{1}}}}}\times{T}_{{2}}={\frac{{{5}}}{{{293}}}}\times{493}={8.41}\)

(b)The pressure of the gas at P\(\displaystyle{220}^{\circ}{C}\)

\(\displaystyle{P}_{{2}}={\frac{{{P}_{{1}}{V}_{{1}}}}{{{V}_{{2}}}}}={\frac{{{1}\times{5}}}{{{8.41}}}}={0.59}\)

Force acting on the piston

\(\displaystyle{F}={P}\times{A}={0.59}\times{101.325}\times{10}^{{3}}\times{0.01}\)

\(\displaystyle={597.81}\) N

Displacement of the piston

\(\displaystyle{x}={\frac{{\text{Force}}}{{\text{force constant}}}}={\frac{{{F}}}{{{K}}}}={\frac{{{597.81}}}{{{2.00}\times{10}^{{3}}}}}={0.293}\)

\(\displaystyle{m}={29.3}{c}{m}\)