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Why is the change in entropy equation for a change in temperature sometimes written and sometimes written ? Do you always multiply the Cv/Cp by moles? In Example 9.2 in the book they say C=nCv,m. I was just wondering if anyone can clarify this for me? Thanks!
This depends on which C you're using. When you have to multiply C by n, it means that C is the specific heat per mole of substance, and when you don't, it's just specific heat. You can also tell if you look at the units; specific heat per mole will be in J/mol, while specific heat will just be J.
When it says "C" without any subscript, it signifies heat capacity, as an extensive property. This is not as common in application; an intensive property is more applicable as it can be applied to any amount of a substance. So we either divide it by the mass or moles of a sample to get specific heat capacity or molar heat capacity respectively and make it intensive. This is so the exact value can be found experimentally for a certain substance and put in a table to be used later. It is this specific or molar heat capacity (with subscripts "s" and "m" respectively) that is used typically in equations, and in that case you have to multiply it by the amount of substance because the specific heat capacity is only per gram, and molar heat capacity is only per mole.
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