20090104

Physics final exam question: mass density of gases

Physics 205A Final Exam, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 13.10

[10 points.] Suppose there are two tanks of identical volume, one containing H2 molecules and the other He atoms. The two gases are at the same temperature and pressure. Which has the higher mass per volume density (or are they equal)? Explain your answer using the ideal gas law and properties of ideal gases.

Solution and grading rubric:
  • p = 10/10:
    Correct. Identical pressures, volumes, and temperatures means that both tanks hold the same number of particles. Since an He atom has more mass than an H_2 molecule, then the He tank will have the greater mass per volume density.
  • r = 8/10:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May only indirectly imply that the number of particles is the same.
  • t = 6/10:
    Nearly correct, but argument has conceptual errors, or is incomplete. Does not discuss how it is that the tanks have the same number of particles, directly arguing from greater molar mass for He atoms; or says that mass per volume will be the same due to the same number of particles for either tank.
  • v = 4/10:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Uses equipartition (mode-counting) and/or fact that He and H_2 are monatomic and diatomic, respectively.
  • x = 2/10:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y = 1/10:
    Irrelevant discussion/effectively blank.
  • z = 0/10:
    Blank.

Grading distribution:
Sections 70854, 70855
p: 9 students
r: 4 students
t: 16 students
v: 7 students
x: 2 students
y: 0 students
z: 1 student

A sample of a "p" response (from student 0013):

A sample of a "t" response (from student 1863) confusing number density with mass density:

A sample of a "v" response (from student 1001) appealing to equipartition:

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