A sinker of weight `w_0` has an apparent weight `w_1` when weighed in a liquid at a temperature `t_1 and w_2` when weight in the same liquid at temperature `t_2`. The coefficient of cubical expansion of the material of sinker is `beta`. What is the coefficient of volume expansion of the liquid.

Explanation

Let `theta=T_2-T_1` and `gamma=`coefficient of volume expansion of liquid.
Let density of liquid at temperatures `T_1` and `T_2` be `rho_1` and `rho_2`,
respectively.
`impliesrho_1=rho_2(1+gammatheta)` .(i)
Let `V_1` and `V_2` be the volumes of the sinker at temperatures `T_1` and `T_2`, respectively.
`impliesV_2=V_1(1+gamma_stheta)` ..(ii)
The loss in weight at `T_1=V_1rho_1gimpliesW_0-W_1=V_1rho_1g` ..(iii)
The loss in weight at `T_2=V_2rho_2gimpliesW_0-W_2=V_2rho_2g`....(iv)
Dividint. (iii) by Eq. (iv), `(W_0-W_1)/(W_0-W_2)=(V_1rho_1)/(V_2rho_2)`
Using Eqs. (i) and (ii), `(W_0-W_1)/(W_0-W_2)=(1+gammatheta)/(1+gamma_stheta)`
`implies1+gammatheta=(W_0-W_1)/(W_0-W_2)+gamma_s((W_0-W_1)/(W_0-W_2))theta`
`impliesgamma=((W_2-W_1)/(W_0-W_2))(1)/(T_2-T_1)+((W_0-W_1)/(W_0o-W_2))gamma_s`