1. An ideal gas expands at a constant pressure of 6.00 x 10 5 Pa from a volume o

Question

1. An ideal gas expands at a constant pressure of 6.00 x 105 Pa from a volume of 1.00 m3 to a volume of 4.00 m3 and then is compressed to one-third that pressure and a volume of 2.50 m3 as shown in the figure below before returning to its initial state. How much work is done in taking a gas through one cycle of the process shown in the figure?

2. The work done by an engine equals one-fourth the energy it absorbs from a reservoir.

(a) What is its thermal efficiency?

(b) What fraction of the energy absorbed is expelled to the cold reservoir?

Explanation / Answer

Part 1:

Since dU is a state function and when the gas reaches its initial condition, then dU=0 and net work done in the complete cycle is given by the area of the PV diagram.

So net area of the triangle = 0.5*3*4 x 105 Pa m3 = 6*105 Pa m3 = 6*105 joules.

6*105J is the work done by the gas, since the direction of cycle is clockwise.

Part 2:

a) Only 1/4 of the heat/thermal energy is used to run the engine. 1/4 = 0.25

Efficiency = 0.25

b) if 1/4 of the heat is obsorbed by the engine then the rest must be expelled.

Hence,

1 - 1/4 = 3/4.

3/4 is expelled to the cold reservoir.

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