The related equations are : `Q=mc(T_(2)-T_(1)), l_(1)=l_(0)[1+alpha(T_(2)-T_(1))]` and `PV-nRT`,
where the symbols have their usual meanings. Find the dimension of
(A) specific heat capacity (C) (B) coefficient of linear expansion `(alpha)` and (C) the gas constant (R).

Answer

`[c]=[L^(2)T^(-2)K^(-1)], [alpha]=[K^(-1)], [R]=[M^(1)L^(2)T^(-2)K^(-1) mol^(-1)]`

Explanation

(i)`c=Q/(m[T_2-T_1]`
Dimension of c`=[M^1L^2T^(-2))/([M^1L^0T^0][M^0L^0T^0K^1])`
`=[L^2T^(-2)K^(-1)]`
(ii)`alpha=(l_1-l_0)/(l_0(T_2-T_1))`
`implies` Dimension of `alpha=[M^0L^1T^(0))/([M^0L^1T^0][M^0L^0T^0K^1])`
(iii)`R=(PV)/(nT)=([M^1L^(-1)T^(-2)][L^3])/([mol][K])=[M^1L^2T^(-2)K^(-1)mol^(-1)]`