Find the dimensional formulae of the following quantites:
(a) the specific heat s
(b) the gas constant `R`
(c) the Boltzmann constant k
(d) the latent heat L
(e) the coefficient of linear expansion alpha
(f) Stefan 's constant sigma
(g) Wien 's constant b
some formulae involving these quantities are
`Q=ms Deltatheta, PV =nRT,PV=NkT, Q=mL`
`Deltal= l alpha Deltatheta,u=sigmaAT^(4),lambdaT=b`
where `Q`: heat, `m`: mass, `Deltatheta`: temperature difference,
`P`: pressure, `V`: volume, `n`: number of moles, `T`: temperature,
`N`: number of molecules, `l`: length, `u`: energy/time, `A`: area and `lambda`: wavelength.

Explanation

(a) `Q = ms Deltatheta rArr s =(Q)/(mDeltatheta)`
`[s]=(ML^(2))/(M K)=L^(2) T^(-2) K^(-1)`
(b) `PV=nRT rArr R=(PV)/(nT)`
`[R]=(ML^(-1) T^(-2) L^(3))/(mol K)=ML^(2) T^(-2) k^(-1) (mol)^(-1)`
(c) `PV=NkT rArr k=(PV)/(NT)`
`[k] = (ML^(-1) T^(-1)L^(-3))/(k)=ML^(2) T^(-2) K^(-1)`
(d) `Q=mL rArrL=(Q)/(m)`
`[L]=(ML^(2)T^(-2))/(M)=L^(2)T^(-2)`
(e) `Deltal = lalphaDeltatheta rArr alpha =(Deltal)/(lDeltatheta)`
`[alpha]=(L)/(LK)=K^(-1)`
(f) `u=sigmaAT^(4)rArr sigma=(u)/(AT^(4))`
`[sigma]=(ML^(2)T^(2)IT)/(L^(2)K^(4))=MT^(-3)K^(-4)`
(g) `lambdaT=brArrb=lambdaT`
`[b]=LK`