NTA Abhyas JEE Main2020PhysicsThermal Properties of MatterPractice
A fluid having a thermal coefficient of volume expansion γ is filled in a cylindrical vessel up to a height h 0 . The coefficient of linear thermal expansion of the material of the vessel is α . If the fluid is heated with the vessel, then find the level of liquid when the temperature increases by Δ θ .
Options
- Ah 0 ( 1 + γΔθ ) ( 1 + 2 αΔθ )
- Bh 0 ( 1 + γΔθ ) ( 1 + 3 αΔθ )
- Ch 0 ( 1 + γΔθ ) ( 1 + αΔθ )
- Dh 0 ( 1 + γΔθ )
Correct answer
A. h 0 ( 1 + γΔθ ) ( 1 + 2 αΔθ )
Step-by-step solution
A base = A 0 1 + βΔ T = A 0 ( 1 + 2 αΔθ   ) V fluid = V 0 1 + γΔ T = A 0 h 0 ( 1 + γΔθ ) A h = A 0 1 + 2 αΔθ h = A 0 h 0 ( 1 + γΔθ ) h = h 0 ( 1 + γΔθ ) ( 1 + 2 αΔθ )