Physics clicker question: molecular rms speeds

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

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 13.1 (extended)

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

[0.6 participation points.] Which type of air molecule has the fastest rms speed at room temperature?
(A) CO2.
(B) H2O.
(C) N2.
(D) O2.
(E) (I'm lost, and don't know how to answer this.)

Sections 0906, 0907
(A) : 5 students
(B) : 9 students
(C) : 14 students
(D) : 4 students
(E) : 0 students

This question was asked again after displaying the tallied results with the lack of consensus, with the following results. No comments were made by the instructor, in order to see if students were going to be able to discuss and determine the correct answer among themselves.

Sections 0906, 0907
(A) : 5 students
(B) : 14 students
(C) : 9 students
(D) : 2 students
(E) : 0 students

Correct answer: (B)

The rms speed of a particle is given by:

v_rms = sqrt(3*k*T/m),

where k is Boltzmann's constant, T is the absolute temperature (in Kelvin), and m is the particle mass (in kg). In unified atomic mass units, the masses of these molecules are 44 u, 18 u, 28 u, and 32 u, respectively, making H2O (the lightest molecular mass in this list) the molecule with the fastest rms speed.