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# Thermodynamics and Fluid Mechanics Quiz for AP Physics B & C (page 2)

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By — McGraw-Hill Professional
Updated on Feb 14, 2011

1. ΔL = αLoΔTThe units of α can be figured out by solving for
2. The units of length cancel, and we're left with 1/K or 1/°C. (Either kelvins or degrees Celsius are acceptable here because only a change in temperature appears in the equation, not an absolute temperature.)

3. U = NkBT. Internal energy is 3/2 times the number of molecules in the gas times Boltzmann's constant (which is on the constant sheet) times the absolute temperature, in kelvins. Or, U = nRT is correct, too, because NkB = nR. (Capital N represents the number of molecules; small n represents the number of moles.)
4. kB is Boltzmann's constant, T is absolute temperature in kelvins, and m is the mass of each molecule in kilograms (NOT in amu!)

5. Change in internal energy is equal to (say it in rhythm, now) "heat added to, plus work done on" a gas. Each term is a form of energy, so has units of joules.

6. The isotherm labeled as "2" is at the higher temperature because it's farther from the origin.
7. Let's put the initially room-temperature gas into a boiling water bath, adding heat. But let's also make the piston on the gas cylinder expand, so that the gas does work. By the first law of thermodynamics, if the gas does as much or more work than the heat added to it, then ΔU will be zero or negative, meaning the gas's temperature stayed the same or went down.
8. (a) Find the area under the graph. (b) Use PV= nRT to find the temperature at each point; then, use U= nRT to find the internal energy at each point; then subtract to find ΔU. (c) You can NOT use the graph to determine heat added or removed. The only way to find Q is to find ΔU and W.
9. For an ideal heat engine.
10. A real heat engine will have a smaller efficiency than this.

11.
1. This is valid for a static (not moving) column of fluid.
2. P0 stands for pressure at the top of the fluid; not necessarily, but sometimes, atmospheric pressure.
12. . … the weight of the fluid displaced.
13. Av is the volume flow rate. Fluid can't be created or destroyed; so, unless there's a source or a sink of fluid, total volume flowing past one point in a second must push the same amount of total volume past another downstream point in the same time interval.
14. mass = density · volume.

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