A steel (\alpha = 12 x 10^{-6} ^o C^{-1}) container with a volume of 548 {cm}^3 is filled with oil (\beta = 0.7 x 10^{-3} ^oC^{-1}). If the temperature is increased by 10^oC how much oil overflows?
V_{spillage} =
Vc = Vo + a*(T-To)Vo
Vc=548 + 12*10^-6*(10)*548 = 548.06576 cm^3 = Volume of container after 10oC
increase in temperature.
V = 548 + 7*10^-4*(10)*548 = 551.836 cm^3. = Volume of the oil after a 10oC
increase in temperature.
Vs = 551.836 - 548.06576 = 3.77 cm^3 =
Volume spilled.
To understand how much oil overflows when the temperature increases, we need to consider the thermal expansion of both the steel container and the oil.
First, let's calculate the change in volume of the steel container. We can use the formula:
ΔV_steel = α_steel * V_steel * ΔT
Where:
ΔV_steel is the change in volume of the steel container,
α_steel is the coefficient of linear expansion of the steel,
V_steel is the initial volume of the steel container, and
ΔT is the change in temperature.
Plugging in the given values, we have:
ΔV_steel = (12 x 10^-6 ^oC^-1) * 548 cm^3 * 10^oC
Next, let's calculate the change in volume of the oil. We can use the same formula but with the properties of the oil:
ΔV_oil = β_oil * V_oil * ΔT
Where:
ΔV_oil is the change in volume of the oil,
β_oil is the coefficient of cubic expansion of the oil (since it's a liquid),
V_oil is the initial volume of the oil, and
ΔT is the change in temperature.
Plugging in the given values, we have:
ΔV_oil = (0.7 x 10^-3 ^oC^-1) * 548 cm^3 * 10^oC
Now that we have calculated the change in volume for both the steel container and the oil, we can determine how much oil overflows. The amount of oil that overflows is equal to the difference between the change in volume of the oil and the change in volume of the steel container:
V_spillage = ΔV_oil - ΔV_steel
Substituting the calculated values, we get:
V_spillage = [(0.7 x 10^-3 ^oC^-1) * 548 cm^3 * 10^oC] - [(12 x 10^-6 ^oC^-1) * 548 cm^3 * 10^oC]
Simplifying the expression will give us the final answer for V_spillage.