The coefficient of linear expansion of glass is `alpha_g` per `.^(@)C` and the cubical expansion of mercury is `lamda_m` per `.^(@)C`. The volume of the bulb of a mercury thermometer at `0^@C` is `V_0` and cross section of the capillary is `A_0`. What is the length of mercury column in capillary at `T^@C`, if the mercury just fills the bulb at `0^@C` ?

Options

A. `(V_0T(gamma_m+3alpha_g))/(A_0(1+2alpha_gT))`
B. `(V_0T(gamma_m-3alpha_g))/(A_0(1+2alpha_gT))`
C. `(V_0T(gamma_m+2alpha_g))/(A_0(1+3alpha_gT))`
D. `(V_0T(gamma_m-2alpha_g))/(A_0(1+3alpha_gT))`

Answer

B

Explanation

Expansion in mercury `=V_0gamma_mT`
Expansion in glass bulb`=V_0(3alpha)T`. Apparent expansion in mercury`=V_0gamma_mT-V_0(3alpha)T`
`:. Deltal=(V_0gamma_mT-V_(0)3alphaT)/(A_0(1+2alpha_gT))`
Length of mercury column in capillary is
`h=Deltal=(V_0T(gamma_m-3alpha_g))/(A_0(1+2alpha_gT))`