A container is filled to the brim with 1.4 L of mercury at 20°C. The coefficient of volume expansion of mercury is 1.8☓10-4 (°C)-1. As the temperature of the container and mercury is increased to 51°C, a total of 7.6 mL of mercury spill over the brim of the container. Determine the linear expansion coefficient of the material that makes up the container.
I got 4.885 x10^-6 k^-1
but that was wrong
1.4 * 1.8*10^-4/oC * (51-20)oC = 0.0078 L. = 7.8mL increase in volume.
7.8 - 7,6 = 0.2 mL saved.
1.4 * K * (51-20) = 0.2mL.
K = 4.61^10^-3 /oC,
To determine the linear expansion coefficient of the material that makes up the container, we can use the equation:
ΔV = V₀ * β * ΔT
Where:
ΔV = change in volume
V₀ = initial volume
β = coefficient of volume expansion
ΔT = change in temperature
To calculate the change in volume, we need to convert the spillage volume from mL to liters:
ΔV = 7.6 mL = 7.6 * 10^-3 L
Now we can rearrange the equation to solve for the linear expansion coefficient:
β = ΔV / (V₀ * ΔT)
First, let's calculate the initial volume of the container. We are told that the container is filled to the brim with 1.4 L of mercury at 20°C, so the volume of the container is 1.4 L.
Substituting the values into the equation:
β = (7.6 * 10^-3 L) / (1.4 L * (51°C - 20°C))
β = (7.6 * 10^-3) / (1.4 * 31)
β ≈ 0.016 L / (4.34)
β ≈ 0.00368 (°C)^-1
Thus, the linear expansion coefficient of the material that makes up the container is approximately 0.00368 (°C)^-1.
To determine the linear expansion coefficient of the material that makes up the container, we can use the formula:
V = V0(1 + βΔT)
where:
V is the final volume of the spilled mercury (in this case, 1.4 L + 7.6 mL = 1.4076 L),
V0 is the initial volume of the mercury (1.4 L),
β is the coefficient of volume expansion of mercury (1.8 × 10^-4 (°C)^-1), and
ΔT is the change in temperature (51°C - 20°C = 31°C).
Now, let's rearrange the formula to solve for β:
β = (V / (V0 ΔT)) - 1
Plugging in the values:
β = (1.4076 L / (1.4 L × 31°C)) - 1
β = (1.007 / 43.4) - 1
β ≈ 0.0232 (°C)^-1
So, the linear expansion coefficient of the material that makes up the container is approximately 0.0232 (°C)^-1.