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)
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)
To calculate the mass of mercury remaining in the bottle, we need to consider the change in volume due to temperature and compare it to the change in volume of the glass bottle.
We know the initial mass of the bottle filled with mercury is 500g.
We also know that 243g of mercury is expelled when the temperature is 35°C.
Let's calculate the change in volume of the mercury:
1. The formula for the change in volume due to temperature change is given by: ΔV = V₀ × β × ΔT, where V₀ is the initial volume, β is the cubic expansivity, and ΔT is the change in temperature.
2. We need to convert the mass of mercury to its volume using the density of mercury, which is 13.6 g/cm³. So, V₀ = m/ρ, where m is the initial mass and ρ is the density.
3. Substitute the given values into the equation: V₀ = 500g / 13.6 g/cm³ = 36.76 cm³.
4. The change in temperature is given as 35°C, so ΔT = 35 - 0 = 35 K.
5. The cubic expansivity of mercury is given as 1.8 × 10^(-4) K^(-1). So, β = 1.8 × 10^(-4) K^(-1).
6. Calculate the change in volume of mercury: ΔV = 36.76 cm³ × 1.8 × 10^(-4) K^(-1) × 35 K = 0.023 cm³.
Next, let's calculate the change in volume of the glass bottle:
1. The linear expansivity of glass is given as 8.0 × 10^(-4) K^(-1). So, α = 8.0 × 10^(-4) K^(-1).
2. The initial volume of the glass bottle is the same as the volume of the mercury: V₀ = 36.76 cm³.
3. Calculate the change in volume of the glass bottle: ΔV = V₀ × α × ΔT = 36.76 cm³ × 8.0 × 10^(-4) K^(-1) × 35 K = 0.103 cm³.
Now, let's calculate the mass of the remaining mercury:
1. The total change in volume is given by ΔV_total = ΔV_mercury + ΔV_glass = 0.023 cm³ + 0.103 cm³ = 0.126 cm³.
2. The density of mercury is 13.6 g/cm³. So, the mass of the remaining mercury is m_remaining = ΔV_total × ρ = 0.126 cm³ × 13.6 g/cm³ = 1.714 g.
Therefore, the mass of mercury remaining in the bottle is approximately 1.714g.
To calculate the mass of mercury remaining in the bottle, we need to consider the changes in volume due to temperature changes and the respective expansivities of both mercury and glass.
Here's how you can approach this problem step by step:
1. Determine the change in temperature (ΔT):
ΔT = Final temperature - Initial temperature
ΔT = 35°C - 0°C
ΔT = 35°C
2. Calculate the change in volume of mercury (ΔV_mercury):
Expansion of mercury = cubic expansivity of mercury × initial volume of mercury × ΔT
Expansion of mercury = (1.8×10^(-4) K^(-1)) × initial volume of mercury × ΔT
Expansion of mercury = (1.8×10^(-4) K^(-1)) × V_mercury × ΔT
Expansion of mercury = (1.8×10^(-4) K^(-1)) × (initial mass of mercury / density of mercury) × ΔT
Expansion of mercury = (1.8×10^(-4) K^(-1)) × (500 g / density of mercury) × ΔT
3. Calculate the change in volume of glass (ΔV_glass):
Expansion of glass = linear expansivity of glass × initial volume of glass × ΔT
Expansion of glass = (8.0×10^(-4) K^(-1)) × V_glass × ΔT
Expansion of glass = (8.0×10^(-4) K^(-1)) × (initial mass of glass / density of glass) × ΔT
4. Calculate the change in total volume (ΔV_total):
ΔV_total = ΔV_mercury + ΔV_glass
5. Calculate the final volume of mercury (V_mercury_final):
V_mercury_final = initial volume of mercury + ΔV_mercury
6. Calculate the mass of mercury remaining:
Mass of mercury remaining = V_mercury_final × density of mercury
However, to fully solve this problem, we need the density of both mercury and glass. Please provide the densities so we can complete the calculation for you.