# What is heat capacity?

The **heat capacity** of a body or system is the quotient that results between the heat energy transmitted to that body and the change in temperature that it experiences in that process. Another more precise definition is that it refers to how much heat it is necessary to transmit to a body or system so that its temperature increases one degree kelvin.

It happens continuously that hotter bodies give up heat to cooler bodies in a process that lasts as long as there is a difference in temperature between the two bodies in contact. So, heat is the energy that is transmitted from one system to another by the simple fact that there is a difference in temperature between the two.

By convention, positive heat ( *Q* ) is defined as that which is absorbed by a system, and as negative heat that which is transferred by a system.

From the above it can be deduced that not all objects absorb and conserve heat with the same ease; thus certain materials heat up more easily than others.

It should be taken into account that, ultimately, the heat capacity of a body depends on its nature and composition.

**Formulas, Units, and Measurements**** **

The heat capacity can be determined starting from the following expression:

C = dQ / dT

*If* the temperature change is small enough, the previous expression can be simplified and replaced by the following:

C = Q / ΔT

So, the unit of measurement of heat capacity in the international system is the Joule per kelvin (J / K).

Heat capacity can be measured at constant pressure C _{p} or constant volume C _{v} .

**Specific heat**

Often the heat capacity of a system depends on its quantity of substance or its mass. In this case, when a system is made up of a single substance with homogeneous characteristics, specific heat is required, also called specific heat capacity (c).

Thus, the mass specific heat is the amount of heat that must be supplied to the unit mass of a substance to increase its temperature by one degree kelvin, and can be determined starting from the following expression:

c = Q / m ΔT

In this equation m is the mass of the substance. Therefore, the unit of measurement of specific heat in this case is the Joule per kilogram per kelvin (J / kg K), or also the Joule per gram per kelvin (J / g K).

Similarly, molar specific heat is the amount of heat that must be supplied to a mole of a substance to increase its temperature by one degree kelvin. And it can be determined from the following expression:

*c = Q / n ΔT*

In this expression n is the number of moles of the substance. This implies that the unit of measurement for specific heat in this case is the Joule per mole per kelvin (J / mol K).

**Specific heat of water**

The specific heats of many substances are calculated and easily accessible in tables. The value of the specific heat of water in the liquid state is 1000 calories / kg K = 4186 J / kg K. On the contrary, the specific heat of water in the gaseous state is 2080 J / kg K and in the solid state 2050 J / kg K.

**Heat transfer**

In this way and given that the specific values of the vast majority of substances have already been calculated, it is possible to determine the heat transfer between two bodies or systems with the following expressions:

Q = cm ΔT

Or if molar specific heat is used:

Q = cn ΔT

It should be taken into account that these expressions allow the determination of heat fluxes as long as there is no change of state.

In state change processes we speak of latent heat (L), which is defined as the energy required by a quantity of substance to change phase or state, either from solid to liquid (heat of fusion, L _{f} ) or from liquid to gaseous (heat of vaporization, L _{v} ).

It must be taken into account that such energy in the form of heat is consumed entirely in the phase change and does not reverse a variation in temperature. In such cases the expressions to calculate the heat flux in a vaporization process are the following:

Q = L _{v} m

If molar specific heat is used: Q = L _{v} n

In a fusion process: Q = L _{f} m

If molar specific heat is used: Q = L _{f} n

In general, as with specific heat, the latent heats of most substances are already calculated and are easily accessible in tables. Thus, for example, in the case of water, one has to:

L _{f} = 334 kJ / kg (79.7 cal / g) at 0 ° C; L _{v} = 2257 kJ / kg (539.4 cal / g) at 100 ° C.

**Example**

In the case of water, if a 1 kg mass of frozen water (ice) is heated from a temperature of -25 ºC to a temperature of 125 ºC (water vapor), the heat consumed in the process would be calculated as follows :

**Stage 1**

Ice from -25ºC to 0ºC.

Q = cm ΔT = 2050 1 25 = 51250 J

**Stage 2**

Change of state from ice to liquid water.

Q = L _{f} m = 334000 1 = 334000 J

**Stage 3**

Liquid water from 0ºC to 100ºC.

Q = cm ΔT = 4186 1 100 = 418600 J

**Stage 4**

Change of state from liquid water to water vapor.

Q = L _{v} m = 2257000 1 = 2257000 J

**Stage 5**

Water vapor from 100ºC to 125ºC.

Q = cm ΔT = 2080 1 25 = 52000 J

Thus, the total heat flux in the process is the sum of that produced in each of the five stages and results in 31112850 J.