A 24000 kg subway train initially traveling at 19.5 m/s slows to a stop in a sta

Question

A 24000 kg subway train initially traveling at 19.5 m/s slows to a stop in a 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. Assuming all the work done by the brakes in stopping the train is transferred as heat uniformly to all the air in the station, by how much does the air temperature in the station rise? Take the density of the air to be 1.20 kg/m^3 and its specific heat to be 1020 J/ (kg* K). The answer should be in degrees Celsius. A 24000 kg subway train initially traveling at 19.5 m/s slows to a stop in a 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. Assuming all the work done by the brakes in stopping the train is transferred as heat uniformly to all the air in the station, by how much does the air temperature in the station rise? Take the density of the air to be 1.20 kg/m^3 and its specific heat to be 1020 J/ (kg* K). The answer should be in degrees Celsius. Assuming all the work done by the brakes in stopping the train is transferred as heat uniformly to all the air in the station, by how much does the air temperature in the station rise? Take the density of the air to be 1.20 kg/m^3 and its specific heat to be 1020 J/ (kg* K). The answer should be in degrees Celsius.

Explanation / Answer

Energy=0.5mv^2=4563000 J

let temp rises by T

heat taken by air=mc*T=4563000

m=density*volume=18720 kg

c=1020 J/kg.K

equatting we got

T=0.239 C

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