Question

A student gives the following description of a thermodynamic cycle though which a sample of an ideal monatomic gas is taken. "Initially, the gas has a volume of 1 x 10?³ m³ and a pressure of 1 x 10? Pa. The gas is in a closed cylinder that has a moveable piston on one end. Call the initial state of the gas state A. Process AB takes the gas at constant pressure from state A to state B, where B has three times the volume of state A. The gas is then compressed isothermally until it is back to its initial volume, reaching state C. Finally, a single process CA returns the gas to its initial state." (a) i. On the axes below, plot states A, B, and C, and sketch a graph of pressure P as a function of volume V for cycle ABCA. Label states A, B, and C, and label the axes with numerical values. ii. Let the temperature for state A be T?. In terms of T?, determine the temperature for state B. iii. Compare the temperature at state C to the temperature at state A. Explain how your comparison is consistent with your graph above. (b) i. Briefly describe an experimental procedure that would take the gas from state C to state A. ii. Relate the temperature of the gas to the microscopic processes involved in the energy transfer as the gas goes from state C to state A for the procedure you described in part (b)(i). (c) i. Use the student’s verbal description or your graph in part (a)(i) to calculate a numerical value for the work done on the gas in process AB. ii. The magnitude of the change in internal energy for process AB is |?U| = 300 J. Calculate a numerical value for the energy added to or removed from the gas by heating in process AB.

          A student gives the following description of a thermodynamic cycle though which a sample of an ideal monatomic gas is taken. "Initially, the gas has a volume of 1 x 10?³ m³ and a pressure of 1 x 10? Pa. The gas is in a closed cylinder that has a moveable piston on one end. Call the initial state of the gas state A. Process AB takes the gas at constant pressure from state A to state B, where B has three times the volume of state A. The gas is then compressed isothermally until it is back to its initial volume, reaching state C. Finally, a single process CA returns the gas to its initial state."
(a)
i. On the axes below, plot states A, B, and C, and sketch a graph of pressure P as a function of volume V for cycle ABCA. Label states A, B, and C, and label the axes with numerical values.
ii. Let the temperature for state A be T?. In terms of T?, determine the temperature for state B.
iii. Compare the temperature at state C to the temperature at state A. Explain how your comparison is consistent with your graph above.
(b)
i. Briefly describe an experimental procedure that would take the gas from state C to state A.
ii. Relate the temperature of the gas to the microscopic processes involved in the energy transfer as the gas goes from state C to state A for the procedure you described in part (b)(i).
(c)
i. Use the student’s verbal description or your graph in part (a)(i) to calculate a numerical value for the work done on the gas in process AB.
ii. The magnitude of the change in internal energy for process AB is |?U| = 300 J. Calculate a numerical value for the energy added to or removed from the gas by heating in process AB.

A student gives the following description of a thermodynamic cycle though which a sample of an ideal monatomic gas is taken. "Initially, the gas has a volume of 1 x 10?³ m³ and a pressure of 1 x 10? Pa. The gas is in a closed cylinder that has a moveable piston on one end. Call the initial state of the gas state A. Process AB takes the gas at constant pressure from state A to state B, where B has three times the volume of state A. The gas is then compressed isothermally until it is back to its initial volume, reaching state C. Finally, a single process CA returns the gas to its initial state."
(a)
i. On the axes below, plot states A, B, and C, and sketch a graph of pressure P as a function of volume V for cycle ABCA. Label states A, B, and C, and label the axes with numerical values.
ii. Let the temperature for state A be T?. In terms of T?, determine the temperature for state B.
iii. Compare the temperature at state C to the temperature at state A. Explain how your comparison is consistent with your graph above.
(b)
i. Briefly describe an experimental procedure that would take the gas from state C to state A.
ii. Relate the temperature of the gas to the microscopic processes involved in the energy transfer as the gas goes from state C to state A for the procedure you described in part (b)(i).
(c)
i. Use the student’s verbal description or your graph in part (a)(i) to calculate a numerical value for the work done on the gas in process AB.
ii. The magnitude of the change in internal energy for process AB is |?U| = 300 J. Calculate a numerical value for the energy added to or removed from the gas by heating in process AB.

Added by Kyle M.

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