A temperature rise of 20°C causes mercury to expand and rise 8 cm in a thermometer tube. If the tube cross sectional area is doubled, the mercury will rise by what cm?
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A temperature rise of 20°C causes mercury to expand and rise 8 cm in a thermometer tube. If the tube cross sectional area is doubled, the mercury
Answered by
1
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The change in mercury volume ΔV is proportional to the temperature increase ΔT according to the formula: ΔV = βVΔT. ΔT =20°C .The relation between how much mercury rises in the thermometer Δh and the volume increase ΔV is following
ΔV = A*Δh
Therefore if the tube cross sectional area is doubled A₂ = 2*A₁ then the mercury rise will be twice smaller because ΔV is the same ΔV = A₁*Δh₁ = A₂*Δh₂
A₁* 8 = A₂*Δh₂
A₁* 8 = 2*A₁*Δh₂
Δh₂ = 4 cm
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