An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. The can’s initial volume at 8 °C is 6.9 × 10-4 m3. The coefficient of volume expansion for aluminum is 69 × 10-6 (C°)-1. When the can and the liquid are heated to 89 °C, 5.3 × 10-6 m3 of liquid spills over. What is the coefficient of volume expansion of the liquid?
NOTHING
To find the coefficient of volume expansion of the liquid, we need to use the principle of conservation of volume.
We are given:
- Initial volume of the can: 6.9 × 10^(-4) m^3
- Coefficient of volume expansion for aluminum: 69 × 10^(-6) (C°)^(-1)
- Final temperature: 89 °C
- Spilled volume of liquid: 5.3 × 10^(-6) m^3
First, we need to calculate the change in volume of the can. The change in volume is given by the formula:
ΔV = V * β * ΔT
Where:
ΔV is the change in volume,
V is the initial volume,
β is the coefficient of volume expansion, and
ΔT is the change in temperature.
We are given the initial volume (V) of the can, and the coefficient of volume expansion (β) for aluminum. The change in temperature (ΔT) is the same for both the can and the liquid.
Since the can and the liquid are heated by the same amount, the change in volume of the can will be the same as the change in volume of the liquid. Therefore, the change in volume of the liquid is equal to the spilled volume of the liquid.
So, we have:
ΔV (liquid) = Spilled Volume = 5.3 × 10^(-6) m^3
Next, we need to calculate the change in temperature (ΔT) using the formula:
ΔT = Final Temperature - Initial Temperature
The initial temperature is given as 8 °C and the final temperature is given as 89 °C. Therefore,
ΔT = 89 °C - 8 °C = 81 °C
Now, we are ready to calculate the coefficient of volume expansion of the liquid. Rearranging the formula for change in volume:
β (liquid) = ΔV (liquid) / (V * ΔT)
Plugging in the known values:
β (liquid) = (5.3 × 10^(-6) m^3) / (6.9 × 10^(-4) m^3 * 81 °C)
Calculating the value:
β (liquid) ≈ 8.06 × 10^(-4) (C°)^(-1)
Therefore, the coefficient of volume expansion of the liquid is approximately 8.06 × 10^(-4) (C°)^(-1).