Physics quiz question: units of (mass-specific) heat capacity

Physics 205A Quiz 1, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 1.72

The heat Q (measured in units of kg·m²/s²) extracted from an object of mass m that experiences a temperature decrease ∆T (measured in units of K) can be expressed as:

Q = m·c·∆T.

The units for the heat capacity c are:
(A) kg·m²· s^–2.
(B) kg^-1·m^-2·s².
(C) K·m^-2·s².
(D) K^-1·m²·s^-2.

Correct answer (highlight to unhide): (D)

From the given expression, the units of these quantities are:

(kg·m²/s²) = (kg)·(units of c)·K,

The units of kg cancel on both sides, and dividing both sides by K gives:

m²/(K·s²) = (units of c).

Response (C) is the inverse of response (D). Responses (A) and (B) are inverses of each other, notably with units of kg instead of units of K.

Student responses
Sections 30880, 30881
(A) : 8 students
(B) : 4 students
(C) : 4 students
(D) : 34 students

"Difficulty level": 68%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.77