GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

For a constant pressure process
work done $\left(\mathit{W}\right)=\mathit{p}\left({\mathit{V}}_2-{\mathit{V}}_1\right)$
$\mathit{W}=\mathit{m}\mathit{R}\left({\mathit{T}}_2-{\mathit{T}}_1\right)$
[from ideal gas, eqn. $\mathit{p}\mathit{V}=\mathit{m}\mathit{R}\mathit{T}$ )
$=\mathit{m}\mathit{R}{\mathit{T}}_1\left[\frac{{\mathit{T}}_2}{{\mathit{T}}_1}-1\right]$
$=1\times 0.287\times 400\left[\frac{{\mathit{T}}_2}{{\mathit{T}}_1}-1\right]...\left(\mathit{i}\right)$
Now, at constant pressure, Ideal gas eqn. becomes
$\frac{{\mathit{V}}_2}{{\mathit{V}}_1}=\frac{{\mathit{T}}_2}{{\mathit{T}}_1}$
Since, ${\mathit{V}}_2=2{\mathit{V}}_1$
$\frac{{\mathit{T}}_2}{{\mathit{T}}_1}=\frac{2{\mathit{V}}_1}{{\mathit{V}}_1}$
$\frac{{\mathit{T}}_2}{{\mathit{T}}_1}=2$....(ii)
Putting eqn. (ii) in eqn. (i) we get
$\mathit{W}=1\times 0.287\times 400\left[2-1\right]$
$=114.8\mathit{K}\mathit{J}$