Answer
Given that 1 calorie = 4.2 J = 4.2 kg m2 s–2
Expression for the standard formula for the conversion is as follows –
\[\]\[\frac{Unit(given)}{Unit(new)}={{\left( \frac{{{M}_{1}}}{{{M}_{2}}} \right)}^{x}}{{\left( \frac{{{L}_{1}}}{{{L}_{2}}} \right)}^{y}}{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{z}}\]
Dimension of energy are –
\[\left[ {{M}^{1}}{{L}^{2}}{{T}^{-2}} \right]\]
On comparing this with the formula, we have x = 1, y = 2 and z =- 2
And M1 = 1 kg, L1 = 1m, T1 = 1s
and we are given that M2 = α kg, L2 = β m, T2 = γ s
\[\frac{Calorie}{Unit(new)}=4.2{{\left( \frac{1}{\alpha } \right)}^{1}}{{\left( \frac{1}{\beta } \right)}^{2}}{{\left( \frac{1}{\gamma } \right)}^{-2}}\]
Therefore, Calorie = 4.2 α–1 β–2 γ2