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When a monatomic ideal gas is at constant pressure, the R constant is multiplied by 5/2. When a monatomic ideal gas is at constant volume, it is multiplied by 3/2. I do not believe we need to know where these numbers came from just that we need to use them in these situations of constant pressure or volume with ideal gases. I remember Professor Lavelle saying something about there being a 1/2 value for each axis of a 3-dimensional graph and adding those all together gave the 3/2 number but he said we didn't need to know any specifics.
Both molar heat capacities (Cp= 5/2R and Cv=3/2R) are given constants that can be found on the Constants and Equations sheet that is found on Dr. Lavelle's website and given to us during tests. Also, the R in both constants is the gas constant 8.314 JK^-1mol^-1. For an ideal gas at constant pressure, you would use 5/2 and for an ideal gas at constant volume, you would use 3/2.
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