A glass bottle full of mercury has mass 500 g
On being heated through 35 C, 2.43 g of
mercury are expelled. Calculaté the mass of
mercury remaining in the bottle (cubic
expansivity of mergury is 1.8 x 104 per K.
linear expansivity of glass is 8.0 x 10-6 per
K.
Mass is conserved. The rest is babble.
500 - 2.43 grams
To calculate the mass of mercury remaining in the bottle after being heated, we need to consider two factors: the expansion of mercury and the expansion of glass.
Step 1: Calculate the change in volume of mercury:
We know that the mass of the expelled mercury is 2.43 g. We can use the density of mercury to calculate its volume change.
The density of mercury is approximately 13.6 g/cm³.
So, the change in volume of mercury is: ΔV_mercury = Δm / ρ_mercury
ΔV_mercury = 2.43 g / 13.6 g/cm³
ΔV_mercury = 0.1787 cm³
Step 2: Calculate the change in volume of glass:
The change in temperature is 35 °C. The linear expansion coefficient of glass is 8.0 x 10⁻⁶ per K.
The change in length of glass can be calculated using the formula: ΔL = αLΔT
where:
ΔL is the change in length,
α is the linear expansion coefficient of glass,
L is the original length,
and ΔT is the change in temperature.
Since the glass bottle is in the shape of a cylinder, the change in volume of glass can be calculated as ΔV_glass = πr²ΔL, where r is the radius of the bottle.
Step 3: Calculate the change in volume of the system:
The total change in volume of the system is the sum of the changes in volume of mercury and glass.
ΔV_system = ΔV_mercury + ΔV_glass
Step 4: Calculate the mass of mercury remaining:
The mass of mercury remaining can be calculated using the formula: mass_remaining = original_mass - mass_expelled
Now, let's calculate the values:
Given data:
Original mass of mercury = 500 g
Change in temperature = 35 °C
Cubic expansivity of mercury (β_mercury) = 1.8 x 10⁴ per K
Linear expansivity of glass (α_glass) = 8.0 x 10⁻⁶ per K
Using the formulas and given data, perform the following calculations:
1. Calculate the change in volume of glass:
ΔL = α_glass * L * ΔT
ΔV_glass = π * r² * ΔL
2. Calculate the change in volume of mercury:
ΔV_mercury = Δm / ρ_mercury
3. Calculate the change in volume of the system:
ΔV_system = ΔV_mercury + ΔV_glass
4. Calculate the mass of mercury remaining:
mass_remaining = original_mass - mass_expelled
Please provide the value of the radius (r) of the bottle.
To calculate the mass of mercury remaining in the bottle after being heated, we need to consider the change in volume of both the mercury and the glass bottle due to the increase in temperature.
Let's break down the problem step by step:
Step 1: Calculate the change in volume of the mercury
Using the cubic expansivity (β) of mercury, which is given as 1.8 x 10^4 per K, we can calculate the change in volume (∆V) of the mercury using the formula:
∆V = β * V0 * ∆T
Where:
β = cubic expansivity of mercury = 1.8 x 10^4 per K
V0 = initial volume of mercury = mass of mercury / density of mercury
∆T = change in temperature = 35 °C
Given:
Mass of mercury = 500 g
To calculate the initial volume of mercury, we need to know the density of mercury. Let's assume the density of mercury is 13.6 g/cm³. Therefore,
V0 = 500 g / 13.6 g/cm³ = 36.76 cm³
Now we can calculate the change in volume of mercury (∆V):
∆V = (1.8 x 10^4 per K) * (36.76 cm³) * (35 °C)
∆V = 2.3352 cm³
Step 2: Calculate the change in volume of the glass bottle
Using the linear expansivity (α) of glass, which is given as 8.0 x 10^-6 per K, we can calculate the change in volume (∆Vb) of the glass bottle using the formula:
∆Vb = α * V0b * ∆T
Where:
α = linear expansivity of glass = 8.0 x 10^-6 per K
V0b = initial volume of the glass bottle
We don't have the initial volume of the glass bottle, but we know that the change in volume (∆Vb) is equal to the change in volume of the mercury (∆V). Therefore,
∆Vb = ∆V = 2.3352 cm³
Now we can calculate the initial volume of the glass bottle (V0b):
V0b = ∆Vb / (∆T * α)
V0b = 2.3352 cm³ / (35 °C * 8.0 x 10^-6 per K)
V0b = 8.339 cm³
Step 3: Calculate the mass of the remaining mercury
The mass of the remaining mercury can be calculated by subtracting the expelled mercury from the initial mass of the mercury:
Mass of remaining mercury = Initial mass of mercury - Mass of expelled mercury
Mass of remaining mercury = 500 g - 2.43 g
Mass of remaining mercury = 497.57 g
Therefore, the mass of mercury remaining in the bottle after being heated is approximately 497.57 grams.