(a)
To draw a PV diagram for the gas.
(a)
Answer to Problem 42PQ
The PV diagram for the gas is given below.
Explanation of Solution
It is given that pressure of the gas is
The following figure gives the PV diagram for the gas.
In above figure, point 1 represents the initial state. The gas follows isothermal expansion from
Conclusion:
Thus, the PV diagram for the gas is given below.
(b)
The change in thermal energy.
(b)
Answer to Problem 42PQ
The change in thermal energy of the gas is zero.
Explanation of Solution
From figure its clear that the gas undergoes a
In this problem it is given that the system return’s to its original state. Thus following a cyclic process, total change in thermal energy of the gas is zero.
Conclusion:
Therefore, the change in thermal energy of the gas is zero.
(c)
The work done by environment on the gas.
(c)
Answer to Problem 42PQ
The work done by environment on the gas is
Explanation of Solution
The net work done by the gas is the area inside the curve. In isothermal process volume of the system is raised from
Write the expression for the work done during isothermal expansion.
Here,
Write ideal gas equation.
Here,
Use above equation for the gas at initial state (state 1 in figure).
Here,
Substitute
For isothermal process,
Apply above equation for the isothermal process of the gas.
Here,
Rearrange above equation to get
In figure1, the straight line represents isobaric process where pressure is constant. During this process the system is compressed to original volume. Therefore, work is done on the system.
Write the expression for the work done in isobaric compression.
Here,
The negative sign indicates that work is done on the gas.
During isobaric process, the gas is at pressure
Use above equation to write work done by gas during isobaric compression shown in figure1.
Here,
In an isochoric process total work done is zero.
Write the expression for the total work done by the gas.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the work done by environment on the gas is
(d)
The heat that flows into the gas.
(d)
Answer to Problem 42PQ
The heat that flows into the gas is
Explanation of Solution
Write the first law of
Here,
Since the process is cyclic,
Substitute
Conclusion:
Substitute
Therefore, the heat that flows into the gas is
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Chapter 21 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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