Question

A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m²s^–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α^–1 β^–2 γ² in terms of the new units.

Answer 1

Given that,

1 calorie = 4.2 (1 kg) (1 m²) (1 s^–2)

New unit of mass = α kg

Hence, in terms of the new unit, 1 kg =

In terms of the new unit of length,

And, in terms of the new unit of time,

∴1 calorie = 4.2 (1 α^–1) (1 β^–2) (1 γ²) = 4.2 α^–1 β^–2 γ²