Heat Capacity

One of the easiest ways to measure a heat transfer is to measure a change in temperature and then calculate from that, the heat transferred.  We use the concept of heat capacity to do this.  Heat capacity of a substance describes the amount of heat that can be absorbed by the substance for a given unit rise in temperature (unit = 1 K). It can be expressed in general as:

The Heat capacity can be expressed as a function of the amount of material. The heat capacity per mole is called the molar heat capacity (units J K^-1mol^-1). The heat capacity per gram is called the specific heat capacity (or just specific heat) (units J K^-1g^-1). It can simply be the capacity of the unit object. For example, a calorimeter (made up of or containing several materials, container, insulation, water, etc.) will have a heat capacity unique to it.

It is not completely correct to talk of heat capacity in terms of q since q is not a state function. We are better off using the state functions ΔH rather than q.

We assume that no electrical or mechanical work w’ is being done.

At constant pressure we measure heat as ΔH = q_p and hence the heat capacity we need to use is C_p , where we define:

Thus, we can write (at constant P)

ΔH = C_pΔT

The units of C_p are J/K or J/℃ (remember that ΔT is the same whether its measured in ℃ or in K).  Sometimes, we tabulate heat capacities in per mole or per gram values.  If this is the case, we need to multiply the molar heat capacity by the number of moles or the gram heat capacity (specific heat) by the number of grams to get the total heat capacity. In these cases, we can think of modifying our equation for enthalpy to be

ΔH = nC_pΔT

 (for molar heat capacity values)

OR

ΔH = mC_pΔT (for specific heat values)

Obviously, these equations hold C_p to be independent of temperature.  In reality, while that’s a reasonable estimate for our purposes, it is not strictly correct. The heat capacity of any substance changes slightly with changes in temperature.