Find the dimensions of
a. the specific heat capacity c,
b. the coeficient of linear expansion `alpha` and
c. the gas constant R
Some of the equations involving these quantities are
` Q=mc(T_2-T_1), l_t=l_0[1+alpha(T_2-T_1)] and PV=nRT.`

Answer

A, B, C

Explanation

(a) Specific heat capacity
`C= Q/(m Delta t) = ([ML^2 T^-2])/([M] [K]) = [L^2 T^-2 K^-1]`
(b) Coefficient of linear expansion
`alpha = (L_1 -L_0)/(L_0 Delta T) = ([L])/([LK]) = [K^-1]`
(c) Gas constant
`R= PV/nT = ([ML^-1 T^-2] [L^3])/[(mol)] [K]) = [ML^2 T^-2 K^-1 (mol)^-1 ])`