Let's start with couple of definitions:
- Heat is the amount of energy flowing from one body of matter to another spontaneously due to their temperature difference, or by any means other than through work or the transfer of matter. Historically, many energy units for measurement of heat have been used. The standards-based unit in the International System of Units (SI) is the joule (J).
- Heat capacity – or thermal capacity – is a measurable physical quantity equal to the ratio of the heat added to (or removed from) an object to the resulting temperature change. The specific heat capacity, often called simply specific heat, is the heat capacity per unit mass of a material.
From this definition we have the following formula for specific heat:
where c — specific heat,
Q — heat added or removed to the body,
m — mass of the body,
ΔT — temperature change.
The heat capacity can be affected by many of the variables of state that describe the thermodynamic system under study. These include the starting and ending temperature, as well as the pressure and the volume of the system before and after heat is added. So, the formula below would be somewhat more correct as:
However, in school problems we usually use a constant specific heat at standard pressure. Thus, the relationship between heat and temperature change is usually expressed in the form shown below:
Note that this relationship does not apply if a phase change is encountered, because the heat added or removed during a phase change does not change the temperature.
The calculator below can find the missing value in the formula above, provided that all other values are given. It can find heat added or removed, specific heat, mass, initial temperature or final temperature: