what is relation between alpha,beta,and gamma ?

Alpha = beta/2 and gamma/3
Thanks & Regards
Aarti Gupta
askiitians Faculty

beta=2alpha . gamma=3alpha . alpha:beta:gamma=1:2:3

The relation between superficial thermal expansion coefficient ß and expansion coefficient is given by ß = 2a The relation between bulk thermal expansion coefficient ? and linear expansion coefficient a is given by ? = 3a So, a:ß:? = 1:2:3

Consider a cube of length l, dt is the change in temp, dl is the change in length, ds is the change in area, dv is the change in volume.Linear coefficient of expansion Alpha-α coefficient of area expansion Beta-βcoefficient of volume expansion Gama-γRelation between αandβ :-From thermal expansion of solids,dl=αldt.(1)ds=βsdt..(2)ds=new area - original area=(l+dl)2-l2=l2+2ldl+(dl)2-l2=2ldl( dl is very small and the square of it will be very very small so it can be neglected)=2lαdtl( from (1))=2l2αdt=2sαdt..(3)From (2) and (3)βsdt=2sαdtβ=2α hence, α = β2Relation between a andγ :-dl=αldt.(1)dv=γvdt.(2)dv=new volume-original volume=(l+dl)3-l3=l3+3(l)2dl+3l(dl)2+(dl)3-l3=3l2dl (dl2 and dl3 can be neglected)Substituting dl =αldt=3l22αldt=3l3αdtSince l3 = v=3vαdt..(3)From (2) and (3)γvdt=3vαdtγ=3αα=γ/3SOα=β/2= γ/3