Internal Energy - If you solve this for and , you find...

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Why is for an ideal gas in a thermal process? The total internal energy of an ideal gas can be found by adding the average kinetic energy of all the molecules. This is, therefore, where N is the number of molecules and is the kinetic energy per molecule. But…recall that the kinetic theory of gases is also written with a kinetic energy in it, which is…. (which is derived for a monatomic molecule since you see the 3/2 there). Therefore, we can make the substitution of for the kinetic energy (in red); which becomes . Now, remember both forms of the ideal gas law;
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Unformatted text preview: If you solve this for and , you find that; which will allow the internal energy equation to become the following by the substitution in red; The last step is to realize that is just , the molar specific heat of a monatomic gas. Therefore, the internal energy equation becomes; Which further means that the change of internal energy must be written; which agrees with the familiar equation that we have been using. For further information, please see page 498 in the textbook....
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