Concept explainers
(a)
The temperature and pressure at point C.
(a)
Answer to Problem 11P
The temperature and pressure at point C are
Explanation of Solution
Write the expression for temperature using Ideal gas equation.
Here, T is the temperature, P is the pressure, V is the volume, n is the number of moles and R is the gas constant.
From the graph given in the question, the pressure at point C is 98.0 kPa.
Conclusion:
Substitute 98.0 kPa for P, 2.00 L for V, 0.0200 mol for n and
Therefore, temperature and pressure at point C are
(b)
The change in internal energy of the gas between points A and B.
(b)
Answer to Problem 11P
The change in internal energy of the gas between points A and B is
Explanation of Solution
Write the expression for change in internal energy.
Here,
As the volume is constant, the ideal gas equation can be written as,
Replace
Here,
Conclusion:
Substitute 98.0 kPa for
Therefore, change in internal energy of the gas between points A and B is
(c)
The work done by the gas.
(c)
Answer to Problem 11P
The work done by the gas is
Explanation of Solution
Work done by the gas is equal to the area under the curve. Therefore, work done is equal to the area of triangle ABC. Write the expression for area of triangle ABC.
The length AB is,
The length BC is,
Conclusion:
Substitute 132 kPa for AB and 1.00 L for BC to get W.
Therefore, work done by the gas is
(d)
The total change in internal energy of the gas for one cycle.
(d)
Answer to Problem 11P
The total change in internal energy of the gas for one cycle is
Explanation of Solution
Write the expression for change in internal energy.
Here,
For one complete cycle, the intial and final temperatures are the same. Therefore, change in temperature is zero. As a result, total change in internal energy of the gas is zero.
Conclusion:
Therefore, total change in internal energy of the gas for one cycle is
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