Question

The coefficient of apparent expansion of a liquid is C when heated in a copper vessel and is S when heated in silver vessel. If A is the coefficient of linear expansion of copper, then that of silver is

• A. $\frac{C+S-3A}{3}$
• B. $\frac{C+3A-S}{3}$
• C. $\frac{S+3C-A}{3}$
• D. $\frac{C+2S-3A}{3}$

Answer 1

Answer: (B)

$\frac{C+3A-S}{3}$

Given:

Apparent expansion coefficient of liquid when heated in Copper vessel = C

Coefficient of linear expansion of copper= A

Apparent expansion coefficient of liquid when heated in silver vessel = S

Liquid expansion coefficient = x (say)

Solution:

For copper,

C= x -3A ( volume expansion = 3 × linear expansion)

For silver,

S =x - 3${\alpha }_{Ag}$

Since liquid expansion coefficient is same,

C+ 3A = S+ 3${\alpha }_{Ag}$

$\Rightarrow C+3A-S=3{\alpha }_{Ag}$

$\Rightarrow {\alpha }_{Ag}=\frac{C+3A-S}{3}$

Hence, B is the correct option.