**What is heat capacity?**

The **heat capacity** of a body or system is the quotient 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 by one Kelvin degree.

It continually happens that the hotter bodies give up heat to the colder bodies in a process that continues as long as there is a difference in temperature between the two bodies in contact. Then, heat is the energy that is transmitted from one system to another due to the simple fact that there is a temperature difference between them.

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

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

**Formulas, units and measures**** **

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

C = dQ/dT

If the temperature change is small enough, the above 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 Cp or at constant volume Cv.

**Specific heat**

Often the heat capacity of a system depends on its amount of substance or its mass. In this case, when a system is made up of a single substance with homogeneous characteristics, the specific heat is required, also called the 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 kelvin degree, and it 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 the 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, the molar specific heat is the amount of heat that must be supplied to one mole of a substance to raise its temperature by one degree kelvin. And it can be determined from the following expression:

*c = Q/ n ΔT*

In said expression n is the number of moles of the substance. This implies that the unit of measurement of the 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 are 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 transmission**

In this way and since 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 the molar specific heat is used:

Q = cn ΔT

It must be taken into account that these expressions allow determining the heat flux 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, Lf) or from liquid to gas (heat of vaporization, Lv).

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

Q = Lv m

If the molar specific heat is used: Q = Lv n

In a melting process: Q = Lf m

If the molar specific heat is used: Q = Lf n

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

Lf = 334 kJ/kg (79.7 cal/g) at 0 °C; Lv = 2257 kJ/kg (539.4 cal/g) at 100 °C.

**Example**

In the case of water, if a mass of frozen water (ice) of 1 kg 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 -25 ºC to 0 ºC.

Q = cm ΔT = 2050 1 25 = 51250 J

**Stage 2**

Change of state from ice to liquid water.

Q = Lf m = 334000 1 = 334000 J

**stage 3**

Liquid water from 0 ºC to 100 ºC.

Q = cm ΔT = 4186 1 100 = 418600 J

**stage 4**

Change of state from liquid water to water vapor.

Q = Lv m = 2257000 1 = 2257000 J

**Stage 5**

Water vapor from 100 ºC to 125 ºC.

Q = cm ΔT = 2080 1 25 = 52000 J

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