A piston-cylinder arrangement shown in the figure has a stop located 2 m above the base. The cylinder initially contains air at 140 kPa and 350°C and the piston is resting in equilibrium at a position which is 1 m above the stops. The system is now cooled to the ambient temperature of 25°C. Consider air to be an ideal gas with a value of gas constant R = 0.287 kJ/kgK.

The absolute value of specific work done during the process is ________ kJ/kg. (rounded off to 1 decimal place)

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GATE Mechanical Engineering (ME) Official Paper (Held On: 03 Feb, 2024)
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Answer (Detailed Solution Below) 58.0 - 61.0

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Explanation:

Let Ap be the area of the piston.

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Given : P1 = 140 KPa

T1 = 350°C = 350 + 273 = 623 K

T2 = 25°C = 25+ 273 298 K

W1-s = P1V- PsVs = mR(T1 - Ts)

For constant pressure process:

V ∝ T

⇒ \(\frac{V_{1}}{V_{s}}=\frac{T_{1}}{T_{s}}\)

⇒ \(\frac{A_{p} × 3}{A_{p} × 2}=\frac{623}{T_{s}} \Rightarrow T_{s}=415.33 \mathrm{~K}\)

W1-s = 1 × 0.287 × (623 - 415.33) = 59.60 kJ/kg

Ws-2 = 0 [∵ Constant volume process]

∴ W1-2 = W1-s + Ws-2 = 59.60 + 0 = 59.60 kJ/kg

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