In Figure P19.22, the change in internal energy of a gas that is taken from A to C along the blue path is +800 J. The work done on the gas along the red path ABC is −500 J. (a) How much energy must be added to the system by heat as it goes from A through B to C? (b) If the pressure at point A is five times that of point C, what is the work done on the system in going from C to D?
Figure P19.22
(c) What is the energy exchanged with the surroundings by heat as the gas goes from C to A along the green path? (d) If the change in internal energy in going from point D to point A is +500 J, how much energy must be added to the system by heat as it goes from point C to point D?
(a)
Answer to Problem 20.40P
Explanation of Solution
Given info: The change in internal energy of a gas which is taken along the blue path from A to C is
Write the equation of first law of thermodynamics.
Here,
Write the equation of conservation of energy.
Here,
Substitute
Substitute
Conclusion:
Therefore, the energy which must be added to the system by heat which goes from A through B to C is
(b)
Answer to Problem 20.40P
Explanation of Solution
Given info: The change in internal energy of a gas which is taken along the blue path from A to C is
Write the equation to calculate the work done on the system from C to D.
Here,
Here,
The pressure at point A is five times that of point C.
And the volume is,
Substitute
Substitute
Conclusion:
Therefore, the work done on the system from C to D if pressure at A is five times that of point C is
(c)
Answer to Problem 20.40P
Explanation of Solution
Given info: The change in internal energy of a gas which is taken along the blue path from A to C is
Write the equation of first law of thermodynamics.
Here,
Write the equation to calculate work done along the green path from C to A.
Here, the volume
Substitute 0 for
Substitute
Substitute
Conclusion:
Therefore, the energy exchanged with the surroundings by heat along the green path from C to A is
(d)
Answer to Problem 20.40P
is
Explanation of Solution
Given info: The change in internal energy of a gas which is taken along the blue path from A to C is
Write the equation of first law of thermodynamics.
Here,
Substitute
Conclusion:
Therefore, the energy which must be added to the system by heat which goes from C to D is
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