A specific gravity bottle completely filled with a liquid is heated from 75°C to 100°C. Mass expelled is 1/40 of remaining mass. If apparent cubical expansion coefficient is approximately 10⁻ˣ °C⁻¹, find x.
Physics · Mixed Chapter
JEE Main Practice

Question

A specific gravity bottle completely filled with a liquid is heated from 75°C to 100°C. Mass expelled is 1/40 of remaining mass. If apparent cubical expansion coefficient is approximately 10⁻ˣ °C⁻¹, find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: If remaining mass is m, expelled mass is m/40; fractional apparent increase relative to retained amount is approximately 1/40. Step 2: Temperature rise ΔT = 25°C. Step 3: βapp≈(1/40)/25=1/1000 = 10⁻³ °C⁻¹. Step 4: x=3. (Using total initial liquid mass gives 1/41 rather than 1/40, a small difference.)