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 kg, the unit of length equals m, the unit of time is s. Show that a calorie has a magnitude 4.2 in terms of the new units.

Question

Philoid · Accepted Answer

In this question, we have to apply one of the uses of Dimensional analysis

i.e. Conversion of one system of units into another

Where, n₂ = n₁ × [M₁M₂ ]^a × [L₁/L₂]^b × [T₁/T₂]^c ----------(1)

M_1, L₁, T_{1 =} Fundamental units of one system

M₂, L₂, T₂ = Fundamental units of another system

a,b,c are the dimensions of the quantity in mass, length, and time.

n₁ = numerical value of quantity in one system

n₂ = numerical value of quantity in the other system

The value of 1 calorie in S.I System of units is given. We have to express the value of calorie in another given arbitrary units.

1 calorie = 4.2 J

1 J = 1 kg m² s^–2

Substituting the above values in equation (1).

n₂ = 4.2 []¹ × []² × []^-2

= 4.2 ^-1 ^-2 ²

1 calorie = 4.2 α^-1 β^-2 γ² in new units.

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 kg, the unit of length equals m, the unit of time is s. Show that a calorie has a magnitude 4.2 in terms of the new units.