Test 2 Review Ideal Gas-pv=nrt-watch units

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(b) What is the work done by the gas?

(d) What is the heat injected into the gas during this process?
8. A piston holds an ideal gas consisting of monatomic molecules. The initial. volume is 1.0L. 100J of heat is added to the gas. If the pressure is held constant at 1.010⁵ Pa during this process, what is the final volume?
9. Two separate containers (label them 1 and 2) with the same initial volumes are filled with a diatomic gas such as N₂ at temperature . The molecules do not vibrate internally but may rotate (the case near room temperature). Container 1 is in contact with a thermal reservoir at constant temperature . Container 2 is in complete thermal isolation. The volume of each container is allowed to expand gradually to twice the initial volumes.

(a) Depict the two processes on a single PV diagram.

(b) What is the ratio of the final pressure in container 1 to the final pressure in container 2?
10. A Carnot engine does 400J of work and expels 800J of energy into the cold reservoir on each cycle.

(a) What is the efficiency of the engine?

(b) If of entropy is transferred into the cold reservoir on each cycle, what is the temperature of the hot reservoir?
11. A Carnot cycle on a P-V diagram reaches a maximum volume of 5.0L and a minimum volume of 1.0L. Assume that there is 0.1mol of gas and that .

(a) Find the work done per cycle if the temperatures of the two reservoirs are and .

(b) How much entropy is transferred into the gas while in contact with the hot reservoir?

SOLUTION Multiple choice

1. (a) To keep the pressure constant, the piston does work as the volume increases. Since the gas loses internal energy to do work, the temperature does not increase as much.
2. (c) The ideal gas law shows that density of the air to be proportional to the pressure:

. Therefore, the velocity of sound in air doesn’t change.
3. (a) Adiabatic compression has a steeper curve on the PV diagram with more area under the curve. Since no heat can escape, the gas heats up during the adiabatic compression causing a higher pressure.
4. (e)

5. (a)
1. (a) (linear connection)

2. (a)

(b)

3. (a)

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