Show that for a reversible adiabatic process, PVY is constant for an ideal gas. Note: ● ● ● For ideal gases use the ideal gas law: PV = RT Cp You also need to assume that y = Cy is constant. The assumption that y is constant for an ideal gas is equivalent to the assumption that the heat capacities are constant. This is the only way that the ratio and the difference Cp - Cy Cy can both be constant = y and Cp - Cy=R). In reality, Cp and Cy increase with temperature, but their ratio y is less sensitive to the temperature than the heat capacities themselves.

Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Show that
for a reversible adiabatic process,
Note:
●
●
●
PVY is constant for an ideal
For ideal gases use the ideal gas law: PV = RT
Cp
You also need to assume that y =
Cy
is constant.
gas.
The assumption that y is constant for an ideal gas is equivalent to the assumption that the
heat capacities are constant. This is the only way that the ratio and the difference Cp -
Cv
Cp
Cv
Cy can both be constant ( = y and Cp - Cv = R). In reality, Cp and Cy increase with
temperature, but their ratio y is less sensitive to the temperature than the heat capacities
themselves.
Transcribed Image Text:Show that for a reversible adiabatic process, Note: ● ● ● PVY is constant for an ideal For ideal gases use the ideal gas law: PV = RT Cp You also need to assume that y = Cy is constant. gas. The assumption that y is constant for an ideal gas is equivalent to the assumption that the heat capacities are constant. This is the only way that the ratio and the difference Cp - Cv Cp Cv Cy can both be constant ( = y and Cp - Cv = R). In reality, Cp and Cy increase with temperature, but their ratio y is less sensitive to the temperature than the heat capacities themselves.
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