A calorie is a unit of heat or energy and it equals about 4.2 J where 1J=1kg2/s2. Suppose we employ a system of units in which the units of mass equals α kg, the units 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 and γ2 in terms of the new units.

From standard formula of unit conversion, we know that,

Given unit/New unit = (M1/M2)<sup>2</sup> (L1/L2)<sup>2</sup> (T1/T2)<sup>2</sup>

Dimensional formula of heat = [M)<sup>1</sup>L)<sup>2</sup>T)<sup>-2</sup>]

Therefore, x=1, y=2, and z=2

M1=1kg, L1=1m, T=1s

M2=αkg, L2=βm, T2=γs

1 calorie = 4.2 Joule

1 Joule = 1 kg<sup>2</sup>/s<sup>2</sup>

Calorie/New unit = 4.2(1kg/αkg)<sup>1</sup> (1m/βm)<sup>2</sup> (1s/γs)<sup>-2</sup>

Therefore, Calorie = 4.2 α<sup>-1</sup> β<sup>-2</sup> γ<sup>2</sup> New unit

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