Question

prove that co_efficient of volume expansion is three times the co- efficient of linear expansion

Answer 1

this question is based on thermal expansion .
.linear thermal expansion:-when a solid rod of initial length L is heated through a temperature dT its final length increase is given by
L'=L (1+@dT)
where @ is coefficient of linear expansion .

cubical expansion or volume expansion:-when a solid of initial volume V is heated through a temperature dT ,its final volume increase given by
V'=V (1+¥ dT)
where ¥ is coefficient of volume expansion.

we know Volume of solid object =base area x height =length x width x height
{here we use only for cuboid but this is valid for all solid body}

V=lbh
but we know if temperature increase length width and height all increase linearly so,
V'=l'b'h'
use linear expansion and volume expansion concept
i.e.
V (1+¥ dT)=l (1+@dT) b (1+@dT) h (1+@dT)
=lbh (1+@dT)^3
use binomial expansion concept
here 1>>@dT
so,
V (1+¥ dT)=lbh (1+3@dT)
but V=lbh so put this
V(1+¥ dT)=V (1+3@dT)
now compare LHS to RHS
¥=3@
hence coefficient of volume expansion is 3times coefficient of linear expansion.

Answer 2

Answer:

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