Question

drive the relation between coefficient of real expernsion and liner expension​

Answer 1

Explanation:

Relation between coefficient of linear expansion and coefficient of real expansion:

Consider a thin rectangular parallelopiped solid of length, breadth, height and volume l

at temperature 0

C. Let the solid be heated at some higher temperature say to C.

Let l,b,h,V be the length, breadth, height and volume at temperature to C.

Then the original volume V

o

=l

o

b

o

h

o

....(1)

Consider linear expansion

length l=l

o

(1+αt)

breadth b=b

(1+αt)

height h=h

(1+αt)

where α=coefficient of linear expansion

Final volume V=lbh=l

(1+αt)×b

(1+αt)×h

(1+αt)

(1+3αt+3α + 2t )

2+α x 3t

3\alpha

Now, α is very small hence α 2

is still small, hence quantity α

2t

2α

3 t x 3

can be neglected.

V=V

o

(1+3αt) ....(2)

Considering cubical expansion of the solid

V=V

(1+γt)

From (1) and (2),

γ=3α ....

Hope its help..