A vessel is 80% filled with liquid and has 20% empty space. The empty-space volume remains constant with temperature. If βᵥ/βₗ=4/y, where βᵥ and βₗ are cubical expansion coefficients of vessel and liquid, find y.
Physics · Mixed Chapter
JEE Main Practice

Question

A vessel is 80% filled with liquid and has 20% empty space. The empty-space volume remains constant with temperature. If βᵥ/βₗ=4/y, where βᵥ and βₗ are cubical expansion coefficients of vessel and liquid, find y.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Initially, liquid volume Vₗ=0.8V and vessel capacity V. Step 2: Constant empty volume requires equal absolute expansions ΔVessel=ΔVliquid. Step 3: βᵥVΔT = βₗ(0.8V)ΔT, hence βᵥ/βₗ=0.8=4/5. Step 4: y=5.