A glass bottle full of mercury has mass 500 g. On being heated through 35°C, 2.43 g of mercury are expelled. Calculate the mass of mercury remaining in the bottle (cubic expansivity of mercury is 1.8 x 10-4 per K. linear expansivity of glass is 8.0 x 10-6 per
To solve this problem, we need to consider the change in volume of both mercury and glass when heated and use this information to find the mass of mercury remaining in the bottle.
First, let's determine the change in volume of mercury when heated. We can use the coefficient of cubic expansivity (β) of mercury:
β = 1.8 x 10^-4 per K
The formula to calculate the change in volume (ΔV) of a substance is:
ΔV = V * β * ΔT
where V is the initial volume, β is the coefficient of cubic expansivity, and ΔT is the change in temperature.
Given that ΔT = 35°C and ΔV = 2.43 g, we need to find V.
To find V, we can use the formula for the volume of a right cylinder:
V = π * r^2 * h
where r is the radius and h is the height of the cylinder.
Since we are given the mass of mercury (500 g), we can find its volume using the density (ρ) of mercury:
ρ = m / V
where m is the mass and V is the volume.
Given that the density of mercury is 13.6 g/cm^3, we can rearrange the equation to solve for V:
V = m / ρ
Now, let's calculate the volume of the mercury:
V = 500 g / 13.6 g/cm^3
V = 36.76 cm^3
To find the radius and height of the cylinder, we need additional information. Without this information, we cannot proceed with the calculations.