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F = ma (Final Problems)
Dimensional Analysis
FMA-2011-21 · 2011 F = ma (AAPT)

2011 F = ma Exam — Question 21

21. An engineer is given a fixed volume Vm of metal with which to construct a spherical pressure vessel. Interestingly, assuming the vessel has thin walls and is always pressurized to near its bursting point, the amount of gas the vessel can contain, n (measured in moles), does not depend on the radius r of the vessel; instead it depends only on Vm (measured in m3), the temperature T (measured in K), the ideal gas constant R (measured in J/(K·mol)), and the tensile strength of the metal σ (measured in N/m2). Which of the following gives n in terms of these parameters?
Source: Question 21, 2011 F = ma Exam, © 2011 American Association of Physics Teachers (AAPT) and the U.S. Physics Team. Adapted by PhysicsTrainer: reformatted into a separate question and answer choices for online multiple-choice practice, with answer choices retyped; any shared setup from nearby questions is repeated here. Not affiliated with or endorsed by AAPT or the U.S. Physics Team.