Molar heat capacity

Figure 1. Copper has a molar heat capacity of 24.5 J/mol⋅K, meaning that it requires 24.5 J of energy to heat a mole of copper by one degree Kelvin.[1] To see more examples of molar heat capacities of different substances, visit this HyperPhysics page.

Molar heat capacity is defined as the amount of heat required to raise 1 mole of a substance by 1 degree Kelvin.[2] Molar heat capacity is very similar to specific heat capacity but measures per mole instead of per gram of substance. Molar heat capacity is an intensive property (it doesn’t vary with the amount of substance). The SI unit of molar heat capacity is Joule per mole per Kelvin, [math]\frac{J}{mol⋅K}[/math].[3]

The formula for molar heat capacity is shown below:

[math]c_n=\frac{Q}{n\Delta T}[/math]

where

  • [math]c_n[/math] is the molar heat capacity,
  • [math]Q[/math] is the heat needed (in Joules),
  • [math]n[/math] is the number of moles, and
  • [math]\Delta T[/math] is the change in temperature of the system (in Kelvin).


To find the number of moles ([math]n[/math]) of a substance, divide the mass of the sample (in grams) by its Molar mass (in grams/mol): [math]n=\frac{m}{M}[/math].


The equation for molar heat capacity does not apply if a phase change is occurring, because the heat added or removed during a phase change does not change the temperature.[4]

Further Reading

References

  1. Helmenstine, Todd. "Specific Heat Example Problem." ThoughtCo, Aug. 27, 2020. [Online]. Available: thoughtco.com/specific-heat-example-problem-609531. [Accessed: 12-May-2021]
  2. "What Is Molar Heat Capacity And How Do You Calculate It?" Science ABC, 2021. [Online]. Available: https://www.scienceabc.com/pure-sciences/what-is-molar-heat-capacity-and-how-do-you-calculate-it.html. [Accessed: 12-May-2021]
  3. "Molar heat capacity," Wikipedia, 2021. [Online]. Available: https://en.wikipedia.org/wiki/Molar_heat_capacity. [Accessed: 12-May-2021]
  4. Hyperphysics, Specific Heat [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html