Question

A calorie is a unit of heat or energy and It equals about 4.2 J where 1J = 1 kg m² s^-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 α¹β²γ² in terms of the new units.

Answer 1

1 new unit of mass = α kg

⇒ 1 kg = 1/α new units of mass

1 new unit of length = β m

⇒ 1m = 1/β new units of length

1 new unit of time = γ s

⇒ 1 s = 1/γ new units of time

1 calorie = 4.2 kg m² s^-2 = 4.2^{(1/α) (1/β)^2 (1/γ)^-2}

= 4.2 α^-1 β^-2 γ² in terms of the new units.