A2 Daily A Level Physics question
A small office is approximately 5 m × 4 m × 2.5 m, sealed and well-insulated. A computer setup dissipates 100 W continuously for 1 hour with no other heat sources or sinks. Take air density ≈ 1.2 kg/m^3 and specific heat capacity of air ≈ 1000 J/(kg °C). Ignoring heating of walls/furniture, which estimate is most reasonable for the rise in the air temperature?
Answer
The correct answer is C.
Correct: C — about 6 °C. Room volume ≈ 5×4×2.5 = 50 m^3, so air mass ≈ 50×1.2 = 60 kg; 100 W for 1 hour supplies 100×3600 = 360000 J; temperature rise ≈ 360000 ÷ (60×1000) ≈ 6 °C. A underestimates by roughly a factor of 60, as if 1 hour were treated like about 1 minute. B corresponds to using about 10 minutes (600 s) instead of 1 hour, giving 36000 J and ≈ 1 °C. C is consistent with the mass of air and the full hour of heating in a sealed, insulated room. D overestimates by a factor of 10, as if the air mass were taken as 6 kg (e.g. misplacing a decimal in density or volume).