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Both are forms of heat capacity. Specific heat capacity is the amount of heat required to raise one gram of the substance by one degree Celsius/Kelvin. Molar heat capacity is the amount of heat required to raise one mole of substance by one degree Celsius/Kelvin. Both are intensive properties.
The only difference between the two is that specific heat capacity is per gram of the substance. On the other hand, molar heat capacity is simply measured per mole of the substance. Besides the difference in units, they measure the same thing.
Specific heat capacity is the heat capacity per one gram of a substance. To use this you would need to know how much of a substance you have in terms of its mass. Molar heat capacity is similar but its the heat capacity per one mole of the substance. When using your q=mcdelta(t) equation pay attention to the givens and the units. If you are given grams use specific heat capacity and if you are given moles of a substance use molar heat capacity. If you are given specific heat capacity, but given moles of substance use the molar mass to convert to grams then calculate q.
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