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Explain why an ideal gas taken around a rectangular PV
Chapter 4, Problem 12P(choose chapter or problem)
PROBLEM 12P
Explain why an ideal gas taken around a rectangular PV cycle, as considered in below Problem 1 and Problem 2, cannot be used (in reverse) for refrigeration.
Problem: 1
An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in below Figure. Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes arc “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 Lo 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 yon expected? Explain briefly.
Figure: PV Diagrams
Problem: 2
To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100°C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20°C. After a minute or so, the temperature of the contents of the cup is 24°C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itselfis negligible.
(a) How much heat is gained by the water?
(b) How much heat is lost by the metal?(c) What is the heat capacity of this chunk of metal?(d) If the mass of the chunk of metal is 100 g, what is its specific heat capacity?
Questions & Answers
QUESTION:
PROBLEM 12P
Explain why an ideal gas taken around a rectangular PV cycle, as considered in below Problem 1 and Problem 2, cannot be used (in reverse) for refrigeration.
Problem: 1
An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in below Figure. Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes arc “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 Lo 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 yon expected? Explain briefly.
Figure: PV Diagrams
Problem: 2
To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100°C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20°C. After a minute or so, the temperature of the contents of the cup is 24°C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itselfis negligible.
(a) How much heat is gained by the water?
(b) How much heat is lost by the metal?(c) What is the heat capacity of this chunk of metal?(d) If the mass of the chunk of metal is 100 g, what is its specific heat capacity?ANSWER:
Step 1 of 3
Consider the PV diagram:
From the above PV diagram, the heat must be absorbed in the process A and B. In the process A, pressure is increasing due to heat absorption and in process B, volume expand due to heat absorption.
The heat is expelled throughout the process C and D. in the process C, Volume is decreases due to heat removal and in process D, pressure is decreases due to heat removal.