An aluminum cup is filled to the brim with precisely 0.400 liters of mercury at a temperature of 20 °C. The cup and mercury are then allowed to warm up to a temperature of 50 °C

Calculate the change in volume of the cup and the change in volume of the mercury?
How much mercury over flows the cup?

Acquaint yourself with the coefficient of thermal expansion. For solids, the linear expansion coefficient is usually tabulated. For liquids, it is usually the volume expansion coefficient that you will find in tables.

Subtract the volume expansion of the aluminum from that of the mercury, to get the overflow.

This website should help:
http://physics.info/expansion/

Thanks for the guidelines & reference

20mcubic

To calculate the change in volume of the cup and the change in volume of the mercury, we need to consider the thermal expansion of these substances. The change in volume can be calculated using the formula:

ΔV = V * β * ΔT

where ΔV is the change in volume, V is the initial volume, β is the coefficient of volume expansion, and ΔT is the change in temperature.

For the cup:
Given that the initial volume of the cup is zero and the coefficient of volume expansion of aluminum is 0.0000225/°C, we can calculate the change in volume of the cup as follows:

ΔV_cup = 0 * 0.0000225 * (50 - 20) = 0

Therefore, the change in volume of the cup is 0.

For the mercury:
Given that the initial volume of the mercury is 0.400 liters and the coefficient of volume expansion of mercury is 0.000181/°C, we can calculate the change in volume of the mercury as follows:

ΔV_mercury = 0.400 * 0.000181 * (50 - 20)

ΔV_mercury = 0.400 * 0.000181 * 30 = 0.002184 liters

Therefore, the change in volume of the mercury is 0.002184 liters.

To calculate how much mercury overflows from the cup, we need to compare the final volume of the mercury (including its change in volume) to the initial volume of the cup.

Final volume of the mercury = initial volume of the mercury + change in volume of the mercury
Final volume of the mercury = 0.400 + 0.002184 = 0.402184 liters

Since the initial volume of the cup is zero, the overflow of the mercury is the difference between the final volume of the mercury (0.402184 liters) and the initial volume of the cup (0 liters).

Overflow of mercury = 0.402184 - 0 = 0.402184 liters

Therefore, approximately 0.402 liters of mercury overflows from the cup.