CP A 25,000-kg subway train initially traveling at 15.5 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 and its specific heat to be 1020 J/kg ? K.
Solution 34E Step 1: Mass of the train m = 25000 kg Speed of the train v = 15.5 m/s Density of air = 1.2 Kg/m 3 Specific heat capacity c = 1020 J/Kg.K Dimensions of the station Length = 65 m Width = 20 m Height = 12 m Volume of the station = Length x Width x Height Step 2: Work done to stop the train = heat transferred to station To find the increase in temperature of the station when the brakes radiate heat Step 3: Work done to stop the train = kinetic energy possessed by the train when it is motion 1 2 Kinetic energy = m2 1 2 = 2 *25000 1*.5 5 Kinetic energy = 30x10 J = Q