experiment on polytropic process
Experiment 5
Polytropic Expansion of Air
Object
The object of this experiment is to find the relation between pressure and volume for the expansion of air in a pressure vessel – this expansion is a thermodynamic process.
Introduction
The expansion or compression of a gas can be described by the polytropic relation , where p is pressure, v is specific volume, c is a constant and the exponent n depends on the thermodynamic process. In our experiment compressed air in a steel pressure vessel is discharged to the atmosphere while the air remaining inside expands. Temperature and pressure measurements of the air inside the vessel are recorded. These two measurements are used to produce the polytropic exponent n for the expansion process.
Historical background
Sadi Carnot (1796-1832) [1] in his 1824 "Reflections on the Motive Power of Heat and on Machines Fitted to Develop This Power," examines a reciprocating, piston-in-cylinder engine. Carnot describes a cycle applied to the machine appearing in Figure 5.1, which contains his original sketch. In this figure air is contained in the chamber formed by the piston cd in the cylinder. Two heat reservoirs A and B, with temperature greater than temperature , are available to make contact with cylinder head ab. The reservoirs A and B maintain their respective temperatures during heat transfer to or from the cylinder head.
Carnot gives the following six steps for his machine:
1. The piston is initially at cd when high-temperature reservoir A is brought into contact with the cylinder head ab.
2. There is isothermal expansion to ef
3. Reservoir A is removed and the piston continues to gh and so cools to .
4. Reservoir B makes contact causing isothermal compression from gh to cd.
5. Reservoir B is removed but continual compression from cd to ik causes the temperature to rise to .
6. Reservoir A makes contact, isothermally expanding the air to cd and thus completing the cycle.
Polytropic Expansion of Air
Object
The object of this experiment is to find the relation between pressure and volume for the expansion of air in a pressure vessel – this expansion is a thermodynamic process.
Introduction
The expansion or compression of a gas can be described by the polytropic relation , where p is pressure, v is specific volume, c is a constant and the exponent n depends on the thermodynamic process. In our experiment compressed air in a steel pressure vessel is discharged to the atmosphere while the air remaining inside expands. Temperature and pressure measurements of the air inside the vessel are recorded. These two measurements are used to produce the polytropic exponent n for the expansion process.
Historical background
Sadi Carnot (1796-1832) [1] in his 1824 "Reflections on the Motive Power of Heat and on Machines Fitted to Develop This Power," examines a reciprocating, piston-in-cylinder engine. Carnot describes a cycle applied to the machine appearing in Figure 5.1, which contains his original sketch. In this figure air is contained in the chamber formed by the piston cd in the cylinder. Two heat reservoirs A and B, with temperature greater than temperature , are available to make contact with cylinder head ab. The reservoirs A and B maintain their respective temperatures during heat transfer to or from the cylinder head.
Carnot gives the following six steps for his machine:
1. The piston is initially at cd when high-temperature reservoir A is brought into contact with the cylinder head ab.
2. There is isothermal expansion to ef
3. Reservoir A is removed and the piston continues to gh and so cools to .
4. Reservoir B makes contact causing isothermal compression from gh to cd.
5. Reservoir B is removed but continual compression from cd to ik causes the temperature to rise to .
6. Reservoir A makes contact, isothermally expanding the air to cd and thus completing the cycle.
References: 1. Carnot, S., "Réflexions sur la puissance motive du feu et sur les machines propres à développer cette puissance," Paris, 1824. Reprints in Paris: 1878, 1912, 1953. English translation by R. H. Thurston, "Reflections on the Motive Power of Heat and on Machines Fitted to Develop This Power," ASME, New York, 1943. 2. Clapeyron, E., "Memoir on the Motive Power of Heat," Journal de l 'École Polytechnic, Vol. 14, 1834; translation in E. Mendoza (Ed.) "Reflections on the motive Power of Fire and Other Papers," Dover, New York, 1960. 3. Validyne Engineering Sales Corp., 8626 Wilbur Avenue, Northridge, CA. 91324 http://www.validyne.com/ 4. OMEGA Engineering, INC., One Omega Drive, Stamford, Connecticut 06907-0047 http://www.omega.com/ 5. Wark, K. Jr. & D.E. Richards, Thermodynamics, 6th Ed, WCB McGraw-Hill, Boston, 1999. © 2005 by Ronald S. Mullisen Physical Experiments in Thermodynamics Experiment 5