Question

A calorie is a unit of heat (energy in transit) 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 a kg, the unit of length equals b m, the unit of time is g s. Show that a calorie has a magnitude 4.2 a ¯¹1 b ¯² g² in terms of the new units.

Answer 1

Given, 1 calorie is equal to 4.2 J and 1 J is equal to 1 kg⋅ m 2 ⋅ s −2 .

The units for new employ system is,

New unit of mass =α kg 1 kg= 1 α = α −1

New unit of length =β m 1 m= 1 β = β −1

New unit of time =γ s 1 s= 1 γ = γ −1

The heat or energy for the system is

Q 1 =4.2 J =4.2 kg⋅ m 2 ⋅ s −2 =4.2 ( α −1 )⋅ ( β −1 ) 2 ⋅ ( γ −1 ) −2 =( 4.2 α −1 β −2 γ 2 )

Hence, the magnitude of the heat or energy in calorie for the employ system is 4.2 α −1 β −2 γ 2 .