Isentropic Process (rapid depressurization of a vessel)
Background:
Isentropic (reversible adiabatic) processes are often desired and are often the processes on which device efficiencies are based. One example of a process that approaches being isentropic is the rapid depressurization of gas in a cylinder. This experiment attempts to demonstrate such a process.
Objectives:
To demonstrate a nearly isentropic process and to compare the results of the experiment with the theoretical isentropic process for the gas used in the process.
Assignment:
To measure the transient temperature and pressure decay in a vessel undergoing a nearly isentropic depressurization and to compare with the ideal isentropic temperature versus pressure relationship.
Equipment:
A small pressure vessel with pressure gage and pressurization valve installed at one end, and exhaust valve* and temperature sensor** at the other.
Pressure and temperature readout instruments as available
A pressurized air supply.
* The exhaust valve should be a quick opening valve, such as a ball valve or solenoid valve.
** It is suggested that a bare thermocouple of no larger than about 0.05 mm (2 mil) wire diameter be used, so as to have sufficiently rapid temperature response. This will require either a visual temperature readout or a temperature recorder.
Measurements:
Although the experiment can be performed by manually reading a dial pressure gage and the readout from a thermocouple, having the ability to record and display the pressure and temperature variation with time is a great improvement.
Thus, a record of P and T variation with time is preferred.
Demonstration:
Beginning with a vessel initially pressurized and at nominally room temperature, measure the temperature and pressure after the exhaust valve is opened and the vessel depressurizes quickly toward atmospheric pressure.
Plot the variation of absolute temperature with absolute pressure, and compare the result with that for the air undergoing a reversible adiabatic (isentropic) expansion.
For constant specific heats, the isentropic process results in the relationship:
where T is the absolute temperature at absolute pressure P and Ti and Pi are the initial absolute temperature and absolute pressure, respectively.
The two results could be compared in a plot of T versus P, or the exponent on the pressure ratio could be determined for the experiment and compared to (k-1)/k = 0.286 for air.
If electronic readouts are not available, the final pressure and temperature can be measured at the end of rapid depressurization and compared to the ideal isentropic process values.
Comments:
If the depressurization/venting process occurs very rapidly the temperature sensor may not have fast enough response to follow the temperature decline. This is why a small gage thermocouple is needed. On the other hand, if the process occurs too slowly, heat transfer to the air from the vessel walls will cause the process to deviate from being adiabatic. This can easily occur for the experiment, since we know that if the process is conducted very slowly, the air temperature will remain near room (initial) temperature.
Questions:
How well do the results of this experiment compare with the ideal isentropic theory?
What are some of the sources for error in the experiment, and do these tend to account for the difference observed between the experimental and ideal processes?
