Alpha valuer......

Circumference of a circular ring is C1 at t1°Celsius and C2 at t2°Celsius.Show that coefficient of linear expansion of the material of the ring.

Give the value of α?

C2-C1/C1t1-C2t2 C1-C2/C2t1-C1t2 C2t1-C1t2/C1-C2 C2-C1-t1(C2t1-C1t2)

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1 solution

C1 = Co + (Co)(A)t1 ........(i)
C2 = Co + (Co)(A)t2..........(ii)
Dividing (i) by (ii),
(C1)/(c2) = (1 + A.t1)/(1 + At2) ...........(iii)
From (iii),
A = ( C 1 C 2 ) / ( C 2. t 1 C 1. t 2 ) \boxed{A=(C1-C2)/(C2.t1 - C1.t2)}
Here,
A = Alpha(i.e coefficient of linear expansion),
Co = Circumference of the circular ring at 0 o 0^{o} C

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