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- Thread starter Evilinside
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FredGarvin

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[tex]h = u + \frac{p}{\rho}[/tex] and the form of ideal gas equation of state [tex]p =\rho RT[/tex] You get:

[tex]h = u + RT[/tex]

If you differentiate with respect to temperature:

[tex]dh = du + R dT[/tex]

[tex]\frac{dh}{dT} = \frac{du}{dT} + R[/tex]

From relations for ideal gases...

[tex]C_v = \frac{du}{dT}[/tex] and [tex]C_p = \frac{dh}{dT}[/tex]

we can say that [tex]C_p = C_v + R[/tex] or

[tex]C_p - C_v = R[/tex]

This is important because that says that for all ideal gasses, the difference between [tex]C_p[/tex] and [tex]C_v[/tex] is a constant.

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FredGarvin

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