Question

The height of mercury column measured with brass scale at temperature T₀ is H₀. What height H' will the mercury column have at T = 0°C. Coefficient of volume expansion of mercury is γ. Coefficient of linear expansion of brass is α ______.

Options

• H₀(1 + αT₀)

• `("H"_0(1 + 3alpha"T"_0))/(1+gamma"T"_0)`

• `("H"_0(1 + 3alpha"T"_0))/((1+gamma//3)"T"_0)`

• `("H"_0(1 + alpha"T"_0))/(1+gamma"T"_0)`

Answer 1

The height of mercury column measured with brass scale at temperature T₀ is H₀. What height H' will the mercury column have at T = 0°C. Coefficient of volume expansion of mercury is γ. Coefficient of linear expansion of brass is α `bb(("H"_0(1 + alpha"T"_0))/(1+gamma"T"_0))`.

Explanation:

P_atm = ρ₀gH;

P_atm = `(rho_0  "gH"_0)/(1+gamma"T"_0)`

H `→` true reading at T₀°C

Let H₀ be observed reading at T₀°C

∴ H₀ = H[1 - αT₁]

ρ₀gH' = `(rho_0"gH"_0[1+alpha"T"_0])/(1+gamma"T"_0)`

⇒ H' = `("H"_0(1 + alpha"T"_0))/(1+gamma"T"_0)`