A class of 100 students taking an exam has a power output per student of about 1

Question

A class of 100 students taking an exam has a power output per student of about 10 W. Assume that the initial temperature of the room is 20 degrees C and that its dimensions are 6.0m by 15.0m by 3.0m. What is the temperature of the room at the end of 2.0 hours if all the heat remains in the air in the room and none is added by an outside source? The specific heat of air is 837 J/kgC and its density is about 1.3x10^-3 g/cm^3. Assume that the body temperature of the students is constant.

a) 31 degrees C b) 27 degrees C c) 35 degrees C d) 45 degrees C

Please show step by step solutions and clearly indicate formulas used. The correct answer is 44.5 degrees C.

Explanation / Answer

total power output = 100 x 10 = 1000W

heat released in 2 hours = P x t = 1000 x (2x 3600 sec) = 72 x 10^5 J

volume of room = 6 x 15 x 3 = 270 m^3

mass = volume x density = 270 x (1.3 x 10^-3 x 10^-3 kg / 10^-6 m^3) = 351 kg

Q = m s deltaT

72 x 10^5 = 351 x 837 x (T - 20)

T = 44.51 deg C Or 45 deg C

Ans(d)

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