Question

The mechanical equivalent of heat

(a) has the same dimension as heat
(b) has the same dimension as work
(c) has the same dimension as energy
(d) is dimensionless

Answer 1

(d) is dimensionless

If the mechanical work done (W) produces the same temperature change as heat (H), then the mechanical equivalent of heat (J) is equal to W/H. Thus,

J = W/H

Since the unit of work and heat is the same, mechanical equivalent of heat is dimensionless.