Temperature Changes in an Ideal Gas

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In this Demonstration, an ideal gas is heated or cooled in two containers, one at constant pressure and one at constant volume. You can vary the amount of heat added or removed with the slider. After setting "heat gas" or "cool gas", click the play button to the right of "add heat" or "remove heat" to initiate heat transfer. The first law and the ideal gas law are used to calculate the final temperature and the changes in internal energy () and enthalpy () for each system. The work is calculated for the constant-pressure process, and the final pressure is calculated for the constant-volume system.

Contributed by: Rachael L. Baumann (June 2015)
Additional contributions by: John L. Falconer
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA



The final temperatures of the constant-pressure and constant-volume systems are found using:


where is the change in internal energy, is the heat added or removed and is work, all in kJ/mol.

For the constant-volume process: .

For the constant-pressure process: or ,

so ,

and so for a constant-pressure process.

Here is pressure (Pa), is molar volume (), is the ideal gas constant, is the temperature in K and is the enthalpy change (kJ/mol).

For both processes:





where and are the constant-volume and constant-pressure heat capacities (kJ/[mol K]).

The ideal gas law is used to calculate the final volume for the constant-pressure process and the final pressure for the constant-volume process:

for constant pressure,

for constant volume.

The screencast video at [1] explains how to use this Demonstration.


[1] Temperature Changes in an Ideal Gas [Video]. (Sep 1, 2016) www.colorado.edu/learncheme/thermodynamics/TemperatureChangesinIdealGas.xhtml.

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