PhysicsBowl 2019 Q40

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PhysicsBowl 2019

40) We want to find out how high the mercury will rise when heated. This problem expects us to use concepts of volume expansion to figure this out. We can start by writing out the formula for volume expansion.

Where V is volume, β is the thermal expansion coefficient, V[o] is the initial volume, and T is temperature

Our next step is to convert and use the given values to find the change in volume. Note that it is convenient to try to find the change volume in mm^3 because the cross-sectional area is given in mm^2.

Where V is volume, β is the thermal expansion coefficient, V[o] is the initial volume, and T is temperature

Now that we know the change in volume, we can easily find the change in height. By simply using dimensional analysis, we can come up with a formula to find the change in height.

Where h is height, V is volume, and A is cross-sectional area

Answer: D