A barometer with brass scale calibrated at 0°C reads 75.000 cm at 20°C. Find its corrected 0°C mercury reading (cm). Given βₘ=0.00018 °C⁻¹ for mercury and αᵦ=0.0000189 °C⁻¹ for brass.
Physics · Mixed Chapter
JEE Main Practice

Question

A barometer with brass scale calibrated at 0°C reads 75.000 cm at 20°C. Find its corrected 0°C mercury reading (cm). Given βₘ=0.00018 °C⁻¹ for mercury and αᵦ=0.0000189 °C⁻¹ for brass.

G1 Physics · Accepted Answer

Step 1: The actual physical mercury height at 20°C is 75.000(1+αᵦ×20). Step 2: For an equivalent 0°C mercury column, account for temperature dependence of mercury density. Step 3: h₀≈75[1+αᵦ(20)]/[1+βₘ(20)]. Step 4: h₀≈75(1.000378)/(1.0036)≈74.759 cm, matching printed 74.758 cm to rounding.