The total energy of a blackbody radiation source is collected for one minute and used to heat water. The temperature of the water increases from 20.0oC to 20.5oC. If the absolute temperature of the blackbody is doubled and the experiment repeated, which of the following statements would be most nearly correct?
A. The temperature of the water would increase from 20oC to 21oC
B. The temperature of the water would increase from 20oC to 24oC
C. The temperature of the water would increase from 20oC to 28oC
D. The temperature of the water would increase from 20oC to 36oC
E. The water would boil within the one-minute time period.
(GR9277 #14)
Solution:
Blackbody Radiation (Stefan-Boltzmann Law): u = σT4 → u ∝ T4
u1 ∝ T4 and u2 ∝ (2T)4
Heat Transfer: Q = mcΔT → Q ∝ ΔT
Q1 ∝ ΔT1 = 20.5 − 20 = 0.5
u1/u2 = Q1/Q2
T4/16T4 = 0.5/ΔT2
ΔT2 = 16 × 0.5 = 8
Answer: C
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