NTA Abhyas JEE Main2020PhysicsThermal Properties of MatterPractice
The apparent coefficients of volume expansion of a liquid filled in vessel A and B of identical volumes are found to be γ 1 and γ 2 , respectively. If α 1 be the coefficient of linear expansion of A then the coefficient of linear expansion of B will be
Options
- Aγ 1 - γ 2 3 - α 1
- Bγ 2 - γ 1 3 + α 1
- Cγ 2 - γ 1 3 - α 1
- Dγ 1 - γ 2 3 + α 1
Correct answer
B. γ 2 - γ 1 3 + α 1
Step-by-step solution
Let V be the volume of the liquid and Δ T the rise in temperature. Since apparent expansion = true expansion - expansion of vessel ∴    V γ 1 Δ T = V γ Δ T-V 3 α 1 Δ T or, γ 1 = γ + 3 α 1 ...(i) (for vessel A) and γ 2 = γ + 3 α 2 ...(ii) (for vessel B) where γ is the coefficient of real expansion of the liquid. Subtracting Eq. (ii) from Eq. (i), γ 1 - γ 2 = 3 α 1 - α 2 or, α 1 - α 2 = γ 1 -