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Why are heat capacities extensive, but specific and molar heat capacities intensive properties?
Heat capacities change based on the amount of particles. Specific and molar heat capacities are for specified quantities of particles, so they are intensive.
Look at the units- specific heat capacity is typically in units of J/g*C, and molar heat capacity is typically in units of J/Kmol. This means that in order to find the actual amount of heat energy in Joules, you need to multiply SHC by temperature and mass, and you need to multiply MHC by temperature and # of moles. With generic heat capacity, you only need to multiply by temperature to get Joules.
The value of the heat capacity will change depending on how much of the substance there is, while the specific heat capacity will always remain constant regardless of how much stuff you have.
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