A glass bottle full of mercury has a mass of 50g. On being heated through 35 degree Celsius, 2.43g of mercury are expelled. Calculate the mass of mercury remaining in the bottle. Cubic expansivity of mercury is 1.8 X 10^-4/k. Linear expansivity of glass is 8.0 X 10^-4/k.
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what is the mass remaining
To calculate the mass of mercury remaining in the bottle, we need to use the concept of thermal expansion.
First, let's calculate the change in volume of the mercury due to the increase in temperature. We can use the formula:
ΔV = V0 * β * ΔT
Where:
- ΔV is the change in volume
- V0 is the initial volume
- β is the cubic expansivity coefficient of mercury
- ΔT is the change in temperature
Given:
- β (cubic expansivity coefficient) = 1.8 x 10^-4 /k
- ΔT (change in temperature) = 35 °C
Since the volume of the mercury expelled is equal to the change in volume, we can calculate it using the given mass of expelled mercury and its density:
Volume expelled = (mass expelled) / (density of mercury)
Given:
- Mass expelled = 2.43 g
- Density of mercury = we can assume the density of mercury remains constant at 13.6 g/cm³
With these calculations, we can determine the initial volume of mercury and then subtract the volume expelled to find the remaining volume. Finally, calculating the mass of the mercury remaining can be done using the density of mercury:
Mass remaining = (Volume remaining) * (density of mercury)
Let's calculate step by step:
1. Calculate the change in volume of mercury using the cubic expansivity formula:
ΔV = V0 * β * ΔT
= V0 * (1.8 x 10^-4 /k) * (35 °C)
2. Calculate the initial volume of mercury using the given mass:
Volume expelled = (mass expelled) / (density of mercury)
Volume expelled = 2.43 g / 13.6 g/cm³
3. Calculate the remaining volume by subtracting the volume expelled from the initial volume:
Volume remaining = V0 - Volume expelled
4. Calculate the mass remaining by multiplying the remaining volume by the density of mercury:
Mass remaining = (Volume remaining) * (density of mercury)
By following these steps, we can determine the mass of mercury remaining in the bottle.