(a)
The pressures and volumes at points
(a)
Answer to Problem 81CP
Pressure at
Explanation of Solution
It is given that pressure at
Write ideal gas equation.
Here,
Rearrange above equation to get
Use equation (II) to get pressure at point
Here,
Use equation (II) to get pressure at point
Here,
Write the condition of isothermal process.
The curve
Use equation (V) for the points
Here,
Write the condition of adiabatic process.
Here,
The curve
Use equation (VII) for the points
Rearrange above equation to get
Substitute
The curve
Use equation (V) for the points
Here,
The curve
Use equation (VII) for the points
Rearrange above equation to get
Substitute
Conclusion:
For ideal gas the value of
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the pressure at
(b)
The net work done per cycle.
(b)
Answer to Problem 81CP
The net work done per cycle is
Explanation of Solution
In the Carnot cycle energy is added by heat to the gas during isothermal expansion, in the figure it is the process
Write the expression for work done by the gas.
Here,
Write the relation between heat added and work done according to first law of thermodynamics.
Here,
The energy added by heat during the process
Write the expression for the Carnot efficiency.
Here,
Write the expression for the efficiency of the in terms of work done.
Here,
Conclusion:
Substitute
Substitute
Since heat added to gas is equal to
Substitute
Substitute
Therefore, the net work done per cycle is
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Chapter 22 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
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