Heat is a form of energy exchange between the system and its surroundings due to a temperature difference. Thermodynamic systems do not have heat, they have energy, and one of the ways in which they exchange this energy is heat.

Heat always flows from the higher-temperature body to the lower-temperature body until thermal equilibrium is reached, at which time the temperatures of both bodies are equal.

Heat transfer can not only cause changes in temperature, it can also lead to changes in the state of aggregation of matter, fusion of solids, vaporization of liquids... During these phase changes, the temperature remains constant, using the heat energy in overcoming the forces of interaction between the molecules that make up the solid, in the case of fusion. In vaporization, heat energy is used to overcome the forces between liquid molecules and allow them to pass into the vapor phase.

The amount of heat that must be supplied to a substance to change its temperature will depend on:

• the change in temperature that the substance undergoes.
• the mass of substance
• the type of substance

Taking these three factors into account, we can formulate the following equation:

$q=mc_e\Delta T$

Being:

$q$: amount of heat needed to raise the body's temperature by $\Delta T$

$m$: mass of the body.

$c_e$: specific heat of the body.

$\Delta T$: temperature change.

Let's see an example:

How much heat is needed to raise the temperature of 100 g of water from 20 to 80ºC? The specific heat of water is 4.18 J/gºC.

We apply the equation $q=mc_e \Delta T$.

Where:

$m=100\;g$

$c_e=4.18\;J/gºC$

$\Delta T=80-20=60\;ºC$

$q=100\;g\cdot 4.18\;J/gºC \cdot 60ºC=25080\;J$

Sign criteria :

In the equation $q=mc_e\Delta T$, when there is a rise in temperature in the body $\Delta T>0$, for which the heat exchanged has a positive sign $q>0$, it is heat that enters the system increasing its temperature.

In the event that there is a decrease in the system temperature $\Delta T<0$ and $q<0$, in this case the heat leaves the system towards the environment.

Summarizing:

• $q>0$, if the heat goes from the system to the surroundings (heat absorbed by the system).
• $q<0$, if the heat goes from the environment to the system (heat given up by the system)

Another concept of great importance is the law of conservation of energy . In the interactions between the system and the environment, energy is conserved. The energy that the system gives up is absorbed by the environment and vice versa. This law of energy conservation can be expressed in the form of heat exchanged between the system and the environment as follows:

$q_{system}+q_{environment}=0$

Equivalent to:

$q_{system}=-q_{environment}$

The heat given off by the system is gained by its surroundings and vice versa.