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An ideal diatomic gas, in a cylinder with a movable
Chapter 1, Problem 34P(choose chapter or problem)
Problem 34P
An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in Figure. Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes are “frozen out.” Also assume that the only type of work done on the gas is quasistatic compression-expansion work.
(a) For each of the four steps A through D, compute the work done on the gas, the heat added to the gas, and the change in the energy content of the gas. Express all answers in terms of P1, P2, V1 and V2. (Hint: Compute ΔU before Q, using the ideal gas law and the equipartition theorem.)
(b) Describe in words what is physically being done during each of the four steps, for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed.
(c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as you expected? Explain briefly.
Figure: PV diagrams
Questions & Answers
QUESTION:
Problem 34P
An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in Figure. Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes are “frozen out.” Also assume that the only type of work done on the gas is quasistatic compression-expansion work.
(a) For each of the four steps A through D, compute the work done on the gas, the heat added to the gas, and the change in the energy content of the gas. Express all answers in terms of P1, P2, V1 and V2. (Hint: Compute ΔU before Q, using the ideal gas law and the equipartition theorem.)
(b) Describe in words what is physically being done during each of the four steps, for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed.
(c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as you expected? Explain briefly.
Figure: PV diagrams
ANSWER:
Problem 34P
Solution 34 P
Step 1 :
In this question, we need to find work done on the gas (W), heat added (Q) and change in the energy content of the gas
We need to express these terms of
In the second part, we need to explain in words the physical steps when the piston is held fixed
In the third part,
We need to find the net work done on the gas,net heat added on the gas, net change in energy during entire cycle
Considering the PV diagram given