Question

A capillary tube of area of cross–section a is filled with a mercury column of length L as shown in Fig. The increase in length of mercury column when temperature increases by Δθ is 

( α = coefficient of linear expansion of capillary, γ = coefficient of cubical expansion of mercury)

(1) L(γ - α) Δθ 

(2) L(γ + α) Δθ 

(3) L(γ - 2α) Δθ  

(4) L(γ + 2α) Δθ

Answer 1

(3) L(γ - 2α) Δθ  

When temperature increases by Δθ ; let ‘a’ and ‘L’ be the area of cross–section of tube and length of mercury column.

V' = volume of mercury column when temperature increases = a'L'

V = The initial volume of mercury column = a.L

We have

Using Binomial expansion and retaining first order terms, we have

The increase in length of mercury column = L ' L

= L(γ - 2α) Δθ