# Mechanical Equivalent of Heat

The conversion factor between the two energy units calorie and the Joule is not arbitrarily chosen.

We have just learned that a calorie is the amount of heat that is required to raise the temperature of 1g of water by 1°C. And we also know that

1 J = 1 kg $\cdot$ m2/s2

If we can convert mechanical energy into heat, then there must be a way to measure the relationship between a Joule and a calorie.

Indeed, this can be measured and was first done by James Prescott Joule in 1842, whose accomplishment was honored by the energy-SI unit being named after him. The presently accepted result is:

1 cal = 4.1868 J

Joule's apparatus is schematically shown in this graphic. In this apparatus, the weight is pulled downward by gravity. The mechanical work done on this system is converted to heat by the paddles driven through the water. Once the paddles come to a rest, all of the gravitational energy has gone into heating the water. The rise in the temperature of the water can then be measured.

This relationship between mechanical and thermal work is called "the mechanical equivalent of heat".

Interestingly enough, Joule was not the first who obtained the correct value for the the mechanical equivalent of heat. Earlier in the same year, the young German physician (yes, "physician", not physicist) Julius Robert Mayer had deduced the same result on purely theoretical grounds. But his results were ignored until Joule presented his clearly obtained experimental evidence.