Project ForgeA rigid tank of volume of 8 m³ is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature inside the pipeline are maintained at 600 kPa and 306 K, respectively. The filling of the tank begins by opening the valve and the process ends when the tank pressure is equal to the pipeline pressure. During the filling process, heat loss to the surrounding is 1000 kJ. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kg.K and 0.718 kJ/kg.K, respectively. Neglect changes in kinetic energy and potential energy. The final temperature of the tank after the completion of the filling process is _________ K (round off to the nearest integer).
Explanation
Uniform-flow energy balance for filling an evacuated rigid tank (m1=0, no work): m2u2 = m2h_pipe + Q, with Q=−1000 kJ (heat loss). Substituting m2=P2V/(RT2) with R=cp−cv=0.287 kJ/kg.K: the T2 in m2 and the T2 multiplying cv on the left cancel, giving P2V·cv/R = P2V·cp·T_pipe/(R·T2) + Q. Solving: T2 = (P2V·cp·T_pipe)/(P2V·cv − R·Q) = (4800×1.005×306)/(4800×0.718 − 0.287×(−1000)) = 1,476,144/3733.4 ≈ 395.4 K.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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