GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

Air is held inside a non-insulated cylinder using a piston (mass $\mathit{M}=25\mathit{k}\mathit{g}$ and area $\mathit{A}=100$ ${\mathit{c}\mathit{m}}^2$ ) and stoppers (of negligible area), as shown in the figure. The initial pressure ${\mathit{P}}_{\mathit{i}}$ and temperature ${\mathit{T}}_{\mathit{i}}$ of air inside the cylinder are $200\mathit{k}\mathit{P}\mathit{a}$ and ${400}^{\circ }\mathit{C}$, respectively. The ambient pressure ${\mathit{P}}_{\mathit{\infty }}$ and temperature ${\mathit{T}}_{\mathit{\infty }}$ are $100\mathit{k}\mathit{P}\mathit{a}$ and ${27}^{\circ }\mathit{C}$, respectively. The temperature of the air inside the cylinder $\left({}^{\circ }\mathit{C}\right)$ at which the piston will begin to move is ___________ (correct to two decimal places).