Thermal Physics - Blackbody Radiation

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 20.0^oC to 20.5^oC. 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 20^oC to 21^oC 
B. The temperature of the water would increase from 20^oC to 24^oC
C. The temperature of the water would increase from 20^oC to 28^oC
D. The temperature of the water would increase from 20^oC to 36^oC
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

Thermal Physics - Blackbody Radiation

A blackbody at temperature T₁ radiates energy at a power level of 10 milliwatts (mW). The same blackbody, when at a temperature 2T₁, radiates energy at a power level of 

A. 10 mW
B. 20 mW
C. 40 mW
D. 80 mW
E. 160 mW

(GR8677 #46)

Solution:

Blackbody radiation (Stefan-Boltzmann's law): u = σT⁴

Constant σ = u / T⁴

u₁T₁⁴ = u₂T₂⁴
10 / T₁⁴ = u₂ / (2T₁)⁴
u₂ = (10)(2T₁)⁴ / T₁⁴ = (10)(16) =160

Answer: E

Thermal Physics - Blackbody Radiation

If the absolute temperature of a blackbody is increased by a factor of 3, the energy radiated per second per unit area does which of the following

A. Decreases by a factor of 81
B. Decreases by a factor of 9
C. Increases by a factor of 9
D. Increases by a factor of 27
E. Increases by a factor of 81

(GR0177 #35)

Solution:

Blackbody radiation: u = σT⁴

Thus, if T increases then u (energy) increases
(A) and (B) are FALSE.

The ratio of energy radiated is



Answer: E