A 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Figure P18.63. The process A→B is a reversible isothermal expansion. Calculate (a) the net work done by the gas, (b) the energy added to the gas by heat, (c) the energy exhausted from the gas by heat, and (d) the efficiency of the cycle. (e) Explain how the efficiency compares with that of a Carnot engine operating between the same temperature extremes.
Figure P18.63
(a)
Net work done by the gas.
Answer to Problem 63P
Net work done by the gas is
Explanation of Solution
For an isothermal process AB, the work on the gas is
Here
Write the equation for work done in the process BC,
Here
Work done in the process CA is zero because the volume is constant.
Write the equation for met work done
Conclusion:
Substitute
Substitute
Substitute
Net work done by the gas is
(b)
Energy added to the gas by heat.
Answer to Problem 63P
Total energy absorbed by heat is
Explanation of Solution
The change in internal energy for the process AB is zero as it is isothermal.
Then,
Write the equation for specific heat capacity at constant volume
Here
Write the ideal gas equation in terms of temperature
Similarly,
Here
Write the equation for heat transfer for the process CA,
Substitute (V) in (VIII)
Write the equation for total energy absorbed by heat
Conclusion:
Substitute
Substitute
Substitute
Substitute
Total energy absorbed by heat is
(c)
Energy exhausted from the gas by heat.
Answer to Problem 63P
The energy exhausted is
Explanation of Solution
Write the equation for heat energy transferred
Here
Substitute
Substitute
Conclusion:
Substitute
The energy exhausted is
(d)
Efficiency of the cycle.
Answer to Problem 63P
The efficiency is
Explanation of Solution
Write the equation for efficiency an engine in terms of work done
Here
Conclusion:
Substitute
The efficiency is
(e)
Compare with the efficiency of a Carnot engine.
Answer to Problem 63P
The efficiency of this system is lower than the Carnot engine
Explanation of Solution
Write the equation for efficiency of a Carnot engine
Here
Conclusion:
Substitute
The efficiency of this system is much lower than the Carnot engine
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Chapter 18 Solutions
Principles of Physics
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