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Q. 35

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 596

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Short Answer

FIGURE P21.35 shows a heat engine going through one cycle. The gas is diatomic. The masses are such that when the pin is removed, in steps and , the piston does not move.

a. Draw the diagram for this heat engine.

b. How much work is done per cycle?

c. What is this engine’s thermal efficiency?

a.

The diagram for heat engine is show above

b. The work done per cycle is

c. The thermal efficiency of heat engine is

See the step by step solution

Step by Step Solution

Step : 1 Given Information

The initial temperature is , pressure at point and at point is , the pressure at point and at point is , the volume at point and at point is and the volume at point and at point is .

Step : 2 Explanation of part a

a. Consider the diagram of the engine given below -

From the Figure 1, the process to and to are constant volume process that isochoric process.

Conclusion :

Therefore, the diagram of the heat engine is shown in Figure .

Step : 3 Explanation of part b

The work done is the area of graph.

Substitute for and for in the above equation to find .

Conclusion :

Therefore, the work done per cycle is .

Step : 3 Explanation of part c.

The ideal gas equation at point is written as,

is the process of gas at point .

is the volume of gas at point ,

is the mole number of gas.

is the universal gas constant.

is the initial temperature of gas.

The ideal gas equation at point is written as,

is the pressure of gas at point .

is the finial temperature of gas at point

Substitute for in the above equation.

Substitute for for for and for in above equation to find .

Heat energy is given by,

where for diatomic gas.

The thermal efficiency is given by

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