A 1.00-mol sample of an ideal gas (γ = 1.40) is carried through the Carnot cycle described in Figure 22.11. At point A, the pressure is 25.0 atm and the temperature is 600 K. At point C, the pressure is 1.00 atm and the temperature is 400 K. (a) Determine the pressures and volumes at points A, B, C, and D. (b) Calculate the net work done per cycle.
(a)
The pressure and volume at points
Answer to Problem 22.81CP
For the point
Explanation of Solution
Given data: The number of mole is
Consider the figure of Carnot cycle,
Figure (1)
From the figure, it is clear that the process from
Apply the ideal gas equation for volume at
Here,
The value of ideal gas constant is
Substitute
Thus, the volume at point
Apply the ideal gas equation for volume at
Here,
Substitute
Thus, the volume at point
For the adiabatic process:
The condition is,
Here,
Substitute
Thus, the volume of gas at point
The formula for the pressure at point
Substitute
Thus, the pressure at point
For the adiabatic process:
The condition is,
Here,
Substitute
Thus, the volume of gas at point
The formula for the pressure at point
Substitute
Conclusion:
Therefore, For the point
(b)
The net work done per cycle.
Answer to Problem 22.81CP
The net work done per cycle is
Explanation of Solution
The formula for the net work done per cycle is,
Substitute
Conclusion:
Therefore, the net work done per cycle is
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Physics for Scientists and Engineers
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