# Heat - The mechanical equivalent of heat

Heat is a form of energy transfer from a thermodynamic system to its surroundings (or vice versa) that is not associated with an ordered motion (work) nor an exchange of matter. The heat absorbed or discharged by a thermodynamic system depends in general on the type of thermodynamic process that it has undergone, and it is usually associated (although not always) with a temperature difference between the system and its surroundings.

When a system exchanges heat with its surroundings, the heat is not stored by the system. A system stores energy in the form of internal energy. Heat is therefore an internal energy transfer between a system and its surroundings.

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The SI unit of heat is the joule (J).

When a system exchanges (absorbs or discharges) heat with its surroundings, its temperature generally changes (it increases or decreases). The temperature variation it undergoes depends on the amount of matter the system has, the type of substance and its initial temperature. The physical quantity which reflects this relationship is called the specific heat capacity c. In the SI system:

It is the energy needed to raise the temperature of 1 kg of mass by 1 degree.

The specific heat capacity is an intensive quantity that generally depends on temperature, although for many applications it can be considered approximately constant. From its definition it follows that its SI units are (J/kg K).

If the amount of substance is measured in moles, the corresponding quantity is called the molar heat capacity.

The equation that relates the temperature variation of a system with its mass and with the heat exchanged in a process is:

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The mechanical equivalent of heat

From the end of the 18th century until the middle of the 19th century, several scientists questioned the nature of heat. They proposed several theories and experiments to explain its origin until James Prescott Joule proposed an experiment to demonstrate that heat was just a form of energy that could be obtained from mechanical energy (work).

He devised an experiment to prove that the temperature of water could be raised by transferring mechanical (potential) energy to it. The mechanical energy required to raise the temperature of water from 14.5ºC to 15.5ºC was 4.18 J per gram, thus providing a definition of calorie:

One calorie is the amount of heat needed to raise the temperature of a gram of water from 14.5ºC to 15.5ºC.

It is necessary to specify the temperature since the specific heat capacity of the water depends on it.

Therefore:

Which is the mechanical equivalent of heat.

The energy value that appears on food nutrition labels is expressed in kilocalories (kcal) although these are commonly referred to as calories.

The conversion between kilocalories and calories is:

Sign criteria: The heat absorbed by a system is positive. The heat discharged by a system to its surroundings is negative.

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