# What is Dimensional Formula of Mechanical equivalent of heat?

Posted in Dimensional Formulae | Email This Post |Mechanical equivalent of heat can be defined as the amount of work done to produce a unit quantity of heat. In other words whenever a mechanical work is completely transformed into heat, the amount of heat produced is directly proportional to the amount of work done.

W ∝ Q —— Where W = Amount of Work and Q = units of heat.

W = J Q

In the above equation constant J is Known as Mechanical equivalent of heat or Joule’s equivalent.

From above equation we get,

**Mechanical equivalent of heat (J) = Amount of Work (W) / units of Heat (Q).**

**Dimensional Formula of Work = M ^{1}L^{2}T^{-2}**

**Dimensional Formula of Heat = M**

^{1}L^{2}T^{-2}substituting these values we get,

**Dimensional Formula of Mechanical equivalent of heat (J) = M ^{0}L^{0}T^{-0} . we can also say Mechanical equivalent of heat (J) is dimensionless quantity.**

SI unit of Mechanical equivalent of heat (J) is Joules/calorie (J calorie^{-1} ).