(a)
The unknown pressure, volume and temperature.
(a)
Answer to Problem 16P
The unknown parameters have been tabulated.
State | |||
A | |||
B | |||
C | |||
D |
Explanation of Solution
Consider the first adiabatic process along D through A
Write the equation for adiabatic process,
Here
Rearrange (I) in terms of
Write the ideal gas equation
Here
Substitute for
Consider the isothermal process along C through D.
Therefore,
Here,
Write down the equation for isothermal process.
Here
Substitute (II) in (V)
Consider the adiabatic process along B through C.
Here
Substitute (VI) in (VII)
Consider the isothermal process along A through B
Substitute (IX) in (VIII)
Conclusion:
Substitute
Substitute
Therefore,
Substitute
Substitute
Substitute
Therefore,
State | |||
A | |||
B | |||
C | |||
D |
(b)
Energy, work done and change in internal energy involved in each steps.
(b)
Answer to Problem 16P
Energy, work done and change in internal energy has been tabulated.
Process | |||
A to B | |||
B to C | |||
C to D | |||
D to E |
Explanation of Solution
Consider the isothermal process along A through B.
Write the equation for energy transfer
Here
Then by first law of thermodynamics
Here
Consider the adiabatic process along B through C where
Here
Substitute
Consider the isothermal process along C through D
Consider the adiabatic process along D through A.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore
Process | |||
A to B | |||
B to C | |||
C to D | |||
D to E |
(c)
Efficiency of the engine.
(c)
Answer to Problem 16P
Efficiency is
Explanation of Solution
Write the equation for efficiency
Here
Conclusion:
Refer sub part b and substitute
Efficiency is
(d)
To prove that the efficiency is equal to Carnot efficiency.
(d)
Answer to Problem 16P
The efficiency is equal to Carnot efficiency.
Explanation of Solution
Write the equation for Carnot efficiency
Here
Conclusion:
Substitute
Thus, the efficiency is equal to Carnot efficiency
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Chapter 18 Solutions
Principles of Physics: A Calculus-Based Text
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