Physics quiz question: Boltzmann constant

Physics 205A Quiz 1, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 1.37, 1.39

The Planck temperature T_P (measured in units of K) is given[*] by the expression:

T_P = m_P·c²/k_B.

Planck mass m_P is measured in units of kg, and the speed of light c is measured in units of m·s^–1. The units for the Boltzmann constant k_B are:
(A) kg^–1·m^–2·s²·K.
(B) kg^–1·m²·s^–2·K.
(C) kg·m^–2·s²·K^–1.
(D) kg·m²·s^–2·K^–1.

[*] wki.pe/Planck_temperature.

Correct answer (highlight to unhide): (D)

Replacing the quantities in the equation with their kg, m, s and K units, except for the Boltzmann constant k_B:

K = kg·(m/s)²/k_B,

k_B = kg·m²/(s²·K).

Sections 70854, 70855, 73320
Exam code: quiz01w34K
(A) : 5 students
(B) : 6 students
(C) : 1 student
(D) : 62 students

Success level: 84%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.37