A cylindrical container contains some liquid. The coefficient of linear expansion of the material of the container is `alpha`. When the container is heated it is observed that the liquid level inside the container remains unchanged. What is the volume expansion coefficient of the liquid?

Explanation

Let height of the liquid level inside the container be x and area of cross-section be A.
Now, the level of liquid surface inside the container will remain unchanged when volume expansion of the container due to increase in temperature t = volume expansion of the liquid due to increase in temperature t.
`therefore " " xA times 3alpha times t= xA timesgamma times t`
`" "[gamma=` volume expansion coefficient of the liquid]
`therefore " "gamma=3alpha.`