(a)
The number of moles in the sample.
(a)
Answer to Problem 65AP
The number of moles in the sample is
Explanation of Solution
Write the expression from
Here,
Rearrange the above equation for
Conclusion:
Substitute
Therefore, the number of moles in the sample is
(b)
The temperature of the gas at point B.
(b)
Answer to Problem 65AP
The temperature of the gas at point B is
Explanation of Solution
Write the expression for temperature of the sample gas at point B.
Here,
Conclusion:
Substitute
Therefore, the temperature of the gas at point B is
(c)
The temperature of the gas at point C.
(c)
Answer to Problem 65AP
The temperature of the gas at point C is
Explanation of Solution
The temperature of the gas at point C is equal to the temperature at point B.
Conclusion:
Substitute
Therefore, the temperature of the gas at point C is
(d)
The volume at the point C.
(d)
Answer to Problem 65AP
The volume at the point C is
Explanation of Solution
The figure 1 shows the PV diagram.
Write the expression for volume of the sample gas at point C.
Here,
Conclusion:
Substitute
Therefore, the volume at the point C is
(e)
How to carry out the process
(e)
Answer to Problem 65AP
The process
Explanation of Solution
Conclusion:
(f)
Find
(f)
Answer to Problem 65AP
The
Explanation of Solution
For
Find the internal energy of the gas.
Here,
Find the heat energy for the given process.
For
Find the work done on the gas.
Find the heat energy for the given process.
For
Find the internal energy of the gas.
Find the work done on the gas.
Find the heat energy for the given process.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the
(g)
Find
(g)
Answer to Problem 65AP
The whole cycle process
Explanation of Solution
Find the heat energy for the whole cycle process.
Find the work done on the gas for the whole cycle process.
Find the internal energy of the gas for the whole cycle process.
Conclusion:
Substitute
Substitute
Substitute
Therefore, the whole cycle process
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Chapter 21 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
- A sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P17.68). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state. (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point C. (e) Now consider the processes A B, B C, and C A. Describe how to carry out each process experimentally. (f) Find Q, W, and Eint for each of the processes. (g) For the whole cycle A B C A, find Q, W, and Eint. Figure P17.68arrow_forwardOne mole of an ideal gas does 3 000 J of work on its surroundings as it expands isothermally to a final pressure of 1.00 atm and volume of 25.0 L. Determine (a) the initial volume and (b) the temperature of the gas.arrow_forwardFigure P21.45 shows a cyclic process ABCDA for 1.00 mol of an ideal gas. The gas is initially at Pi = 1.50 105 Pa, Vi = 1.00 103 m3 (point A in Fig. P21.45). a. What is the net work done on the gas during the cycle? b. What is the net amount of energy added by heat to this gas during the cycle? FIGURE P21.45arrow_forward
- 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?arrow_forwardAn ideal gas initially at 300 K undergoes an isobaric expansion at 2.50 kPa. If the volume increases from 1.00 m3 to 3.00 m3 and 12.5 kJ is transferred to the gas by heat, what are (a) the change in its internal energy and (b) its final temperature?arrow_forwardIf a gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred into the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains constant. (e) None of those statements is true.arrow_forward
- When a gas undergoes an adiabatic expansion, which of the following statements is true? (a) The temperature of the gas does not change. (b) No work is done by the gas. (c) No energy is transferred to the gas by heat. (d) The internal energy of the gas does not change. (e) The pressure increases.arrow_forwardA 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. (a) What is the final pressure of the gas? (b) What are the initial and final temperatures? Find (c) Q, (d) Eint, and (e) W for the gas during this process.arrow_forwardThe arrow OA in the PV diagram shown in Figure OQ22.11 represents a reversible adiabatic expansion of an ideal gas. The same sample of gas, starting from the same state O. now undergoes an adiabatic free expansion to the same final volume. What point on the diagram could represent the final state of the gas? (a) the same point A as for the reversible expansion (b) point B (c) point C (d) any of those choices (e) none of those choicesarrow_forward
- You have a particular interest in automobile engines, so you have secured a co-op position at an automobile company while you attend school. Your supervisor is helping you to learn about the operation of an internal combustion engine. She gives you the following assignment, related to a simulation of a new engine she is designing. A gas, beginning at PA = 1.00 atm, VA = 0.500 L, and TA = 27.0C, is compressed from point A on the PV diagram in Figure P19.31 (page 530) to point B. This represents the compression stroke in a fourcycle gasoline engine. At that point, 132 J of energy is delivered to the gas at constant volume, taking the gas to point C. This represents the transformation of potential energy in the gasoline to internal energy when the spark plug fires. Your supervisor tells you that the internal energy of a gas is proportional to temperature (as we shall find in Chapter 20), the internal energy of the gas at point A is 200 J, and she wants to know what the temperature of the gas is at point C. Figure P19.31arrow_forwardA gas in a cylindrical closed container is adiabatically and quasi-statically expanded from a state A (3 MPa, 2 L) to a state B with volume of 6 L along the path 1.8pV= constant. (a) Plot the path in the pV plane. (b) Find the amount of work done by the gas and the change in the internal energy of the gas during the process.arrow_forwardA cylinder is closed at both ends and has insulating EZZ3 walls. It is divided into two compartments by an insulating piston that is perpendicular to the axis of the cylinder as shown in Figure P21.75a. Each compartment contains 1.00 mol of oxygen that behaves as an ideal gas with = 1.40. Initially, the two compartments haw equal volumes and their temperatures are 550 K and 250 K. The piston is then allowed to move slowly parallel to the axis of the cylinder until it comes to rest at an equilibrium position (Fig. P2l.75b). Find the final temperatures in the two compartments.arrow_forward
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