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Enthalpy is the amount of heat released or absorbed in some reaction at a constant pressure, whereas heat capacity is the heat required to raise the temperature of some substance by 1 degree Celsius. In both cases, the units to use are Celsius or Kelvin.
Also, a change in enthalpy means the change in heat of a system. Enthalpy is expressed usually in units such as J or kJ/mol. Heat capacity is calculated by dividing the total energy by the change in temperature. Heat capacity is expressed in J/K or J/degree Celsius.
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