Physics quiz question: comparing rates of radiated heat

Physics 205A Quiz 7, fall semester 2018
Cuesta College, San Luis Obispo, CA

Two solid blocks with the same temperature, but different surface areas and emissivities are placed in separate, room temperature (290 K) environments. Ignore conduction and convection heat transfers to/from the environment. The __________ object radiates more heat per time to the environment.
(A) smaller, e = 0.1.
(B) larger, e = 0.9.
(C) (There is a tie.)
(D) (Not enough information given.)

Correct answer (highlight to unhide): (B)

The power radiated by an object (where the negative sign indicates that heat is continuously leaving its surface) is given by:

Power = –e·σ·A·T⁴,

where the Stefan-Boltzmann constant σ = 5.670×10^–8 watts/(m²·K⁴) and the surface temperatures T = 600 K are the same for both objects.

For the smaller, lower emissitivity (e = 0.1) object, the power radiated is:

Power_smaller = –(0.1)·σ·A_smaller·(600 K)⁴,

and for the larger, higher emissivity (e = 0.9) object, the power radiated is:

Power_larger = –(0.9)·σ·A_larger·(600 K)⁴,

and from inspection, since 0.1 < 0.9 and A_smaller < A_larger, then the larger, higher emissivity object will radiate heat at a higher power rate than the smaller, lower emissivity object.

Sections 70854, 70855
Exam code: quiz07PeA7
(A) : 16 students
(B) : 32 students
(C) : 2 students
(D) : 0 students

Success level: 64%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.37