GATE 2018 ME (ME2) – Question 52
Air is held in a non-insulated cylinder with a piston of mass 25 kg and area 100 cm², initially resting against upper stoppers of negligible area. Initial air pressure is 200 kPa and temperature 400°C. Ambient pressure is 100 kPa and temperature 27°C. Take g = 10 m/s². Find the air temperature (°C) at which the piston begins moving, to two decimal places.
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Correct answer: 145.00 to 150.00
Explanation
Cooling initially occurs at constant volume while the piston touches the upper stops. It starts descending when internal pressure balances atmosphere plus weight: $P^*=100+25(10)/(0.01\times1000)=125$ kPa. For fixed mass and volume, $T^*/T_i=P^*/P_i$. Thus $T^*=(400+273)(125/200)=420.625$ K, or **147.63°C**.