Physics clicker question: heat capacity during phase change

Physics 5A, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 13.11

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the beginning 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) zero.
(B) infinity.
(C) a finite number.
(D) (Not enough information is given.)
(E) (I'm lost, and don't know how to answer this.)

Sections 0906, 0907
(A) : 10 students
(B) : 12 students
(C) : 11 students
(D) : 0 students
(E) : 0 students

Correct answer: (B)

The heat capacity is defined as the ratio of the heat Q (put in) to the resulting temperature increase delta(T):

C = Q/delta(T).

But when heat is put into, or extracted from a system, its temperature remains constant, making delta(T) = 0, and thus its heat capacity will be undefined as it would approach infinity.