The difference in internal energy
Answer to Problem 34P
The difference in internal energy
Explanation of Solution
Since the gas goes through a
Write the equation for the net change in internal energy of the gas.
Here,
The net change in internal energy must be equal to the sum of the change in internal energy of the gas during the different processes in the cycle.
Write the expression for
Here,
Put the above equation in equation (I) and rewrite it for
Write the expression for
Here,
Put the above equation in equation (II).
The process BC is an isochoric process. The work done in an isochoric process is zero. This implies
Write the first law of thermodynamics.
Here,
Use equation (IV) to write the expression for
Here,
The process BC is isobaric.
Write the expression for
Here,
Put the above equation in equation (V).
The process CD is isothermal. The change in internal energy for an isothermal process is zero.
Write the expression for
Use equation (IV) to write the expression for
Here,
The process DA is isobaric.
Write the expression for
Here,
Put the above equation in equation (VIII).
Put equations (VI), (VII) and (IX) in equation (III).
Write the equation for
Here,
Write the equation for
Here,
Conclusion:
It is given that the heat entering the system from B to C is
Substitute
Substitute
Substitute
Therefore, the difference in internal energy
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Chapter 20 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
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