A 25000kg subway train initially travelling at 145 ms slows

A 25,000-kg subway train initially travelling at 14.5 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 61.0 m long by 19.0 m wide by 11.5 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 middot K.___________ degree C

Solution

kinetic energy of the train is converted by the brake to heat to raise the temperature of the air in the station.

KE of train = 1/2 * 25000 * 14.5² = 2628125 J

2628125 J = 1020 * (1.20 * 61 * 19 * 11.5) * delta T

delta T = 0.161 K

That is, the air temperature in the station will rise by 0.161 ⁰C