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A mercury thermometer contains 0.4cm^(3)...

A mercury thermometer contains `0.4cm^(3)` of mercury at `0^(@)C.` The diameter of the capillary tube of the thermometer is 0.2 mm. What should be the length of the scale to measure temperatures between `0^(@)C " to " 100^(@)C`? The coefficient of apparent expansion of mercury `=1.7 times 10^(-4@)C^(-1).`

Text Solution

Verified by Experts

The apparent expansion of mercury due to increase in temperature from `0^(@)C " to " 100^(@)C.`
`" "=0.4 times 1.7 times 10^(-4) times 100=0.0068 cm^(3)`
The cross-section of the capillary tube `=pi(0.01)^(2)cm^(2)`
`therefore` The length of the temperature measuring scale
`" "=0.0068/(pi(0.01)^(2))=21.6 cm.`
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