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The volume expansion coefficients of gla...

The volume expansion coefficients of glass and mercury are `2.4 times 10^(-5@)C^(-1) " and " 1.8 times 10^(-4@)C^(-1)` respectively. What volume of mercury should be kept in the flask so that the volume of the empty space over mercury in the flask remains constant at all temperatures?

Text Solution

Verified by Experts

Let the required volume of mercury = x `cm^(3)` and volume of the glass container = V `cm^(3).`
To keep the volume of empty space constant at any temperature, the expansion of mercury should be equal to that of the glass container for the same rise in temperature.
If the temperature rise in `t^(@)C`,
`" " x times 1.8 times 10^(-4) times t=V times 2.4 times 10^(-5) times t`
or, `" " x=(V times 2.4 times 10^(-5))/(1.8 times 10^(-4))=V times 24/180=2/15V`
`therefore 2/15th` part of the flask should be filled with mercury.
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