A train in a subway with mass 29000 kg enters a subway station with speed 14.5 m
ID: 1781867 • Letter: A
Question
A train in a subway with mass 29000 kg enters a subway station with speed 14.5 m/s . The train slows to a stop in the station and then stays there long enough for its brakes to cool.
The station's dimensions are 65.0 m long by 20.0 m wide by 12.0 m high.
A) Assume that all the work done in stopping the train, which results in raising the temperature of the train's brakes and the subway track, is transferred as heat to the air in the station. If the temperature of the air is raised uniformly (the same throughout the station), by how much does the air temperature in the station rise? Take the density of the air to be 1.20 kg/m3 and its specific heat to be 1020 J/(kgK).
Explanation / Answer
Total kinetic energy is converted to heat energy
E = 0.5 x 29000 x 14.5 x 14.5
E = 304862.5
Mass of air in station
M= 12x20x65x1.2 = 18720kg
From energy transfer equation
E = M x 1020 x T
T = 0.016
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