HEAT CAPACITY of a SYSTEM : (Most General Definition and the one we hardly ever use)

• C_T = Total Amount of Heat Energy required to raise the temperature of some System 1^oC.
• SI: J/ ^oC
  

For such a a system: Q = C_T ΔT

• We hardly ever use this definition because every system would have a different C_T even if it were made of the same substance. For example, a 100g of pure water and 50g of pure water would each have a different total heat capacity. The heat capacity C_T is useful for composite systems composed of different substances like a mixture of a fixed amount of water and copper.

SPECIFIC HEAT CAPACITY of a SUBSTANCE : (Conventionally used in Physics)

• C = Amount of Heat Energy per kilogram that is required to raise the temperature of one kilogram of the substance 1^oC.
• SI: J/(kg⋅^oC) or J/kg/^oC

For such a system: Q = m C ΔT

MOLAR HEAT CAPACITY of a SUBSTANCE : (Routinely used in Chemistry)

• c = Amount of Heat Energy per mole that is required to raise the temperature of 6.022x10²³ molecules of the substance 1^oC.
• SI: J/(mole⋅^oC) or J/mole/^oC

For such a system: Q = n c ΔT

VOLUMETRIC HEAT CAPACITY of a SUBSTANCE : (Commonly used in storage of Solar Energy)

• c_v = Amount of Heat Energy per unit volume that is required to raise the temperature of one cubic meter of the substance 1^oC.
• SI: J/(m³⋅^oC)

For such a system: Q = V c_v ΔT

• Historically, heat capacities have been expressed in ^oC rather than K (Kelvin) because most temperature devices measure temperatures in degrees Celsius. Technically, the units of heat capacity should be expressed in degrees K rather than degrees ^oC. However, ΔT has the same value regardless if T is measured in K or ^oC since the units of K and ^oC have the same size. Thus both system of units will give the same answer.