Your swimming pool is square and 4.9 m on a side. It is 3.9 m deep in the morning. If the temperature changes by 44°C during the afternoon, how much does the depth of the water increase?
To determine how much the depth of the water increases, we need to calculate the thermal expansion coefficient of water and use it to find the change in volume.
1. The thermal expansion coefficient of water is approximately 0.00021 per °C. This means that for every degree Celsius increase in temperature, water expands by 0.00021 times its original volume.
2. Calculate the original volume of water in the pool:
V_original = side^2 * depth
= 4.9 m * 4.9 m * 3.9 m
3. Calculate the change in volume of water due to the temperature change:
ΔV = V_original * (thermal expansion coefficient) * (change in temperature)
= V_original * 0.00021 * 44 °C
4. Calculate the change in depth of water:
Δdepth = ΔV / (side^2)
= ΔV / (4.9 m * 4.9 m)
By plugging in the values obtained in steps 2, 3, and 4, we can find the change in depth of the water in the pool.