Solveeit Logo
Login

Question

Question: The height of mercury column measured with brass scale at temperature T<sub>0</sub> is H<sub>0</sub>...

The height of mercury column measured with brass scale at temperature T0 is H0. What height H' will the mercury column have at T = 0ºC. Coefficient of volume expansion of mercury is g. Coefficient of linear expansion of brass is a -

A

H0(1 + aT0)

B

H0(1+3αT0)1+γT0\frac{H_{0}(1 + 3\alpha T_{0})}{1 + \gamma T_{0}}

C

H0(1+3αT0)(1+γ/3)T0\frac{H_{0}(1 + 3\alpha T_{0})}{(1 + \gamma/3)T_{0}}

D

H0(1+αT0)1+γT0\frac{H_{0}(1 + \alpha T_{0})}{1 + \gamma T_{0}}

Answer

H0(1+αT0)1+γT0\frac{H_{0}(1 + \alpha T_{0})}{1 + \gamma T_{0}}

Explanation

Solution

Patm = r0gH' ; Patm = ρ0gH01+γT0\frac{\rho_{0}gH_{0}}{1 + \gamma T_{0}}

H ® true reading at T0ºC

Let H0 be observed reading at T0ºC

\ H0 = H[1 – aT1]

r0gH' = ρ0gH0[1+αT0]1+γT0\frac{\rho_{0}gH_{0}\lbrack 1 + \alpha T_{0}\rbrack}{1 + \gamma T_{0}} ̃ H' = H0[1+αT1]1+γT1\frac{H_{0}\lbrack 1 + \alpha T_{1}\rbrack}{1 + \gamma T_{1}}