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 8.0×10 ^-6
Can you please shed more light on the answer
the mass mass remaining in the glass
To calculate the mass of the mercury remaining in the bottle after heating, we need to consider the expansion of both the mercury and the glass bottle.
Let's assume the initial mass of the mercury in the bottle is m1 (50g) and the mass expelled is m2 (2.43g). We need to find the mass of the remaining mercury, which is m1 - m2.
First, let's calculate the change in temperature, ΔT. The bottle is heated through 35 degrees Celsius, so ΔT = 35°C.
Next, we'll calculate the change in volume of the mercury. We can use the formula:
ΔV = V * β * ΔT,
where ΔV is the change in volume, V is the initial volume of the mercury, β is the cubic expansivity of mercury, and ΔT is the change in temperature.
We are given that the cubic expansivity of mercury (β) is 1.8 * 10^-4 / K. We need to convert the change in temperature (ΔT) from Celsius to Kelvin. This is done by adding 273 to the Celsius temperature. So, ΔT = 35 + 273 = 308 K.
Now, we can calculate ΔV using the cubic expansivity formula:
ΔV = V * β * ΔT = V * (1.8 * 10^-4 / K) * 308 K.
Next, let's calculate the change in volume of the glass bottle. We can use the formula:
ΔV' = V' * α * ΔT,
where ΔV' is the change in volume of the glass bottle, V' is the initial volume of the bottle, α is the linear expansivity of glass, and ΔT is the change in temperature.
We are given that the linear expansivity of glass (α) is 8.0 * 10^-6 / K.
Since the glass bottle is in direct contact with the mercury, the change in volume of the glass will be the same as the change in volume of the mercury: ΔV' = ΔV.
Now, let's equate the two equations for ΔV and ΔV':
V * (1.8 * 10^-4 / K) * 308 K = V' * (8.0 * 10^-6 / K) * 308 K.
The temperature change (ΔT = 308 K) and the units of Kelvin (K) cancel out, leaving us with:
V * (1.8 * 10^-4) = V' * (8.0 * 10^-6).
Divide both sides of the equation by V' to solve for V:
V / V' = (8.0 * 10^-6) / (1.8 * 10^-4).
V / V' = 0.0444.
Since both V and V' refer to the initial volumes of the mercury and the glass bottle, respectively, the ratio V/V' is equal to the ratio of the initial masses of the mercury and the glass bottle.
Therefore, we can multiply this ratio by the initial mass of the mercury to find the mass of the remaining mercury:
Mass of remaining mercury = m1 - m2 = m1 - (V / V') * m1.
Substituting the known values:
Mass of remaining mercury = 50g - 0.0444 * 50g.
Simplifying:
Mass of remaining mercury = 50g - 2.22g = 47.78g.
Therefore, the mass of the mercury remaining in the bottle after heating is 47.78g.
hey, the mass of Hg did not change
50 - 2.43 = ?????
but it would have been fun to calculate the two volume changes :)