GATE 2024 ME – Question 46

Thermodynamics · Zeroth, first and second laws, work, heat and energy changes · 2 marks · Numerical answer

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/(kg.K).

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

A vertical cylinder with a piston on top. Two stops are fixed 2 m above the base, and the piston initially rests 1 m above the stops.

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Correct answer: 59.30 to 59.90

Explanation

The piston is 3 m above the base at first and the pressure is set by its weight, so it stays at 140 kPa while the air cools and the piston falls. The piston reaches the stops after the height drops from 3 m to 2 m. Further cooling then takes place at constant volume with no work. The work is $w = P(v_1 - v_2)$ with $v_2 = \frac{2}{3}v_1$, so $w = \frac{Pv_1}{3} = \frac{RT_1}{3} = \frac{0.287 \times 623.15}{3} = 59.6$ kJ/kg (done on the air).