Project ForgeAir is held inside a non-insulated cylinder using a piston (mass M=25 kg, area A=100 cm²) and stoppers of negligible area. The initial pressure Pi and temperature Ti of air inside the cylinder are 200 kPa and 400°C, respectively. The ambient pressure P∞ and temperature T∞ are 100 kPa and 27°C, respectively (g=10 m/s²). The temperature of the air inside the cylinder (°C) at which the piston will begin to move is __________ (correct to two decimal places).
Explanation
The piston lifts off the stoppers once the internal pressure falls (as the hot, non-insulated gas cools at constant volume) to the value that just balances the piston's weight plus ambient pressure: P2 = P∞ + Mg/A = 100,000 + (25×10)/0.01 = 100,000+25,000 = 125,000 Pa = 125 kPa. At constant volume, P/T = const: T2 = T1×(P2/P1) = 673.15×(125/200) = 420.72 K = 147.57°C.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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