Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 14.14
[10 points.] Which has the greater molar specific heat—a diatomic gas such as N2, or a monatomic gas such as Ne? Explain your answer using the properties of the specific heats of ideal gases.
Solution and grading rubric:
- p = 10/10:
Correct. A (rigid-bond) diatomic gas molecule can have three modes of translational kinetic energy, as well as two rotation modes, whereas a monoatomic gas atom can only have the three translation kinetic energy modes. Thus a diatomic gas molecule can take in more heat than a monatomic gas atom to produce a given increase in temperature (which is related to an increase in translational kinetic energy). - 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. At least has some discussion of the different number of modes in equipartition. - t = 6/10:
Nearly correct, but argument has conceptual errors, or is incomplete. States that C_V = (5/2)*R for diatomic gas molecules, and C_V = (3/2)*R for monatomic gas atoms, with no discussion of equipartition/modes. - v = 4/10:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May state correct answer with no discussion, or incorrect answer motivated by complexity, molar mass, presence of a bond, relative bond strengths, etc. - 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:
p: 2 students
r: 6 students
t: 10 students
v: 14 students
x: 0 students
y: 1 student
z: 0 students
A sample of a "p" response (from student 1337) is shown below:
A "t" response (from student 1024) where only the correct values for the molar specific heats are cited:
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