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On page 19 in the Course Reader, molar heat capacity is defined as the "heat required to raise temp of one mole by 1 degree Celsius." However, the unit given is J/K/mol. Why are the temperature units different between the definition and the units of molar heat capacity?
Since the molar heat capacity is concerned with a temperature change, it can be expressed in terms of degrees Celsius or degrees Kelvin. Zero degrees Celsius is equal to 273.15 Kelvin, and this difference can be used to calculate degrees Celsius from Kelvin by subtracting this number, and to calculate degrees Kelvin from Celsius by adding this number. Because of this, the temperature change in degrees of either will be the same in degrees Celsius as in Kelvin. In the book on page 267 underneath table 8.2, it says that molar heat capacities commonly use Kelvins. So that is why the units involve Kelvins. The explanation of this in the course reader that uses degrees Celsius actually means the same thing if you insert Kelvins there instead.
I believe molar heat capacity would be considered an intensive property. It is defined as "heat required to raise the temperature of 1 mole of substance by 1 degree Celsius," therefore, since it is the heat needed for SPECIFICALLY 1 mole of substance. Molar heat capacity values do not depend on the amount of substance there is.
Molar heat capacity and specific heat capacity are easy to confuse with heat capacity. Heat capacity is defined as the heat required to raise the temperature of an object by 1°C, and it is extensive because the heat required depends on the amount of substance. Specific heat capacity and molar heat capacity are intensive because they are the heat required to raise the temperature of 1 g of a substance by 1°C and mole of a substance by 1°C, respectively.
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