Find the dimensions of
(a) the specific heat capacity c,
(b) the coefficient of linear expansion `alpha` and
(c) the gas constant R.
Some of the equations these quantities are `Q=mc(T_(2)-T_(1)) l_(t)=l_(0)[1+alpha (T_(2)-T_(1))]` and PV=nRT. (Where Q=heat enegry , m=mass, `T_(1)&T_(2)`= temperatures, `l_(1)` =length at temperature `t^(@)C`, `l_(0)=` length at temperature `0^(@) C`, P=Pressure, v = volume, n = mole)

Answer

(a) `L^(2)T^(-2)K^(-1)` (b) `K^(-1)` (c)`ML^(2)T^(-2)K^(-1)(mol)^(-1)`

Explanation

(a)`[c]=([Q])/([m][T_(2)-T_(1)])`
`[c] =L^(2)T^(-2)k^(-1)`
`[l_(t)]=[l_(0)]=[l_(0)alpha(T_(2)-T_(1))]`
`[alpha]=k^(-1)`
(c) `[R]=([pv])/([nT])=(ML^(-1)T^(-2)L^(3))/(mol K)=ML^(@)T^(-2)k^(-1)k^(-1) mol^(-1)]`