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The calorie is a unit of heat or energy ...

The calorie is a unit of heat or energy and it equals about 4.2 J where `1J=1kgm^(2)s^(-2)`. Suppose we employ a system of units in which the unit of mass equals `alpha` kg, the unit of length equals `beta` m and the unit of time is`gamma` s. Show that the calorie has a magnitude of `4.2alpha^(-1) beta^(-2) gamma^(2)` in terms of the new units.

Text Solution

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Calorie is the of heat energy. Dimensional formula of energy is `ML^(2)T^(-2)`
`n_(1)(M_(1)L_(1)^(2)T_(1)^(-2))=n_(2)(M_(2)L_(2)^(2)T^(-2))`
Given `n_(1)=4.2, n_(2)=?`
`M_(1)=1kgL_(1)=1mT_(1)=1s`
`M_(2)=alpha kg L_(2)=betamT_(2)=gammas`
`n_(2)=n_(1)((M_(1))/(M_(2)))((L_(1))/(L_(2)))^(2)((T_(1))/(T_(2)))^(-2)=4.2(1/(alpha))(1/(beta))^(2)(1/(gamma))^(-2)`
`n_(2)=4.2alpha^(-1)beta^(-2)gamma^(2)`
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