A glass bottle full of mercury has a mass 500g.
35°C, 243g of mercury are
expelled.
Calculate the mass of
f mercury remaining in
the | bottle. (Cubic expansivity. of mercury . is
1.8×x10^-4 K^(-1), linear expansivity .of glass is
8.0×10^(-4)k^(-1)
.......
If you started with 500 grams and expelled 243 grams you are left with
500 grams - 243 grams.
To calculate the mass of the remaining mercury in the bottle, we need to consider the change in volume of the mercury and the glass due to the change in temperature.
First, let's calculate the change in volume of the mercury using its cubic expansivity. The formula to calculate the change in volume is:
ΔV_mercury = V_mercury * β_mercury * ΔT
Where:
ΔV_mercury is the change in volume of the mercury,
V_mercury is the initial volume of the mercury,
β_mercury is the cubic expansivity of mercury, and
ΔT is the change in temperature.
Since we know the initial mass of the mercury (500 grams), we can use its density to find the initial volume:
Density_mercury = mass_mercury / V_mercury
Rearranging the equation, we can find V_mercury:
V_mercury = mass_mercury / Density_mercury
Now we substitute back into the change in volume formula:
ΔV_mercury = (mass_mercury / Density_mercury) * β_mercury * ΔT
Next, let's calculate the change in volume of the glass using its linear expansivity. The formula to calculate the change in volume is:
ΔV_glass = V_glass * α_glass * ΔT
Where:
ΔV_glass is the change in volume of the glass,
V_glass is the initial volume of the glass,
α_glass is the linear expansivity of the glass, and
ΔT is the change in temperature.
The total change in volume is the sum of the change in volume for the mercury and the glass:
ΔV_total = ΔV_mercury + ΔV_glass
Finally, we can calculate the mass of the remaining mercury in the bottle by subtracting the expelled mercury from the initial mass:
mass_remaining_mercury = mass_mercury - mass_expelled_mercury
Note that the given information is missing the quantity of mercury expelled (243g) and the original temperature (35°C). Please provide these values to get the complete solution.