Question

What is the SI unit of mechanical equivalent of heat?

Answer 1

In order to solve this question, we are going to first of all define the mechanical equivalent of heat then, based on the SI units of the factors on which the mechanical equivalent depends, we can write the SI unit of the mechanical equivalent of heat.

Formula used:
The mathematical expression for the mechanical equivalent of heat is
$J = \dfrac{W}{q}$

Complete step-by-step solution:
The mechanical equivalent of heat means that the motion and the heat are interchangeable. A defined amount of energy generates the same amount of work in all situations. In other words, if the work is completely changed to the heat energy, then the same amount of heat is generated. The mathematical expression for the mechanical equivalent of heat is
$J = \dfrac{W}{q}$
Where, $W$is the amount of work required to generate heat while $q$is the amount of heat.
Thus, from the above formula, we can conclude that the mechanical equivalent of the heat has the same SI unit as the work per unit amount of heat. The SI unit of work is Joules per calorie. So, the SI unit of mechanical equivalent of heat is joules per calorie$\left( {Jca{l^{ - 1}}} \right)$.

Note: Alternatively, we can define the mechanical equivalent of heat as the ratio of the $1$ unit of work which is in joules in terms of the SI units to the $1$unit of the heat which is in calories. This makes the SI unit of the mechanical equivalent of heat equal to joules per calorie$\left( {Jca{l^{ - 1}}} \right)$.