Physics clicker question: latent heat

Physics 5A, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Multiple-Choice Question 14.4

Students were asked the following clicker question (Classroom Performance System, einstruction.com) near the start of their learning cycle:

[0.6 participation points.] The heat capacity of a material undergoing a phase change (such as melting/freezing, or boiling/condensing) is typically:
(A) 0.
(B) ∞.
(C) some finite number.
(D) (Not enough information is given.)
(E) (I'm lost, and don't know how to answer this.)

Sections 4987, 4988
(A) : 8 students
(B) : 7 students
(C) : 12 students
(D) : 1 student
(E) : 0 students

Correct answer: (B)

The heat capacity is given by:

C = Q/delta(T).

When heat is put into (or taken from) a system undergoing a phase change, the temperature remains constant, and thus the denominator is zero, making the heat capacity infinite. Thus a system undergoing a phase change cannot have a defined heat capacity, as the heat goes into breaking or making bonds, instead of increasing/decreasing the amount of thermal energy in the system. Instead, the latent heat is defined:

L = Q/m,

where m is the amount of material undergoing a phase change.