Question

what is dimension of mechanical equivalent of heat?

Answer 1

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 = M1L2T-2
Dimensional Formula of Heat = M1L2T-2

substituting these values we get,

Dimensional Formula of Mechanical equivalent of heat (J) = M0L0T-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 ).

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Answer 2

mechanical equivalent of heat can be defined as the amount of work done to produce a unot quantity of heat. In the 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.