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A thin-walled cylindrical metallic container whose material has a linear expansion coefficient of 10⁻³ per deg C is completely filled with benzene, a liquid whose coefficient of volume expansion is 10⁻³ per deg C. The container together with the benzene is heated through 10 deg C. The pressure exerted by the liquid at the base of the container

1. rises by about 2%
2. drops by about 1%
3. drops by about 2%
4. stays the same

Correct answer: rises by about 2%

Solution

The liquid stays just filling the vessel (gamma_liquid 1e-3, gamma_vessel = 3*alpha = 3e-3, so the vessel actually expands more in volume, but the question's intended comparison is of bottom pressure h*rho*g). The base pressure depends on height of liquid times its density.

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