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Many hot-water heating systems have a reservoir tank connected directly to the pipeline to allow for expansion when the water becomes hot. The heating system of a house has 66.9 m of copper pipe with an inside radius of \(8.24 \times 10^{-3}\) m. When the water and pipe are heated from \(22.0^\circ C\) to \(82.1^\circ C\), what must be the minimum volume of the reservoir tank to hold the overflow of water?

Provide your answer in both number and units.

Answer :

The minimum volume of the reservoir tank required to hold the overflow of water is 1.18 m³.

When the water and copper pipe are heated, both expand due to the increase in temperature. The expansion of the water can be calculated using the formula ΔV = βV₀ΔT, where ΔV is the change in volume, β is the volumetric expansion coefficient of water, V₀ is the initial volume, and ΔT is the change in temperature.

The expansion of the copper pipe can be calculated using the formula ΔV = βV₀ΔT, where ΔV is the change in volume, β is the linear expansion coefficient of copper, V₀ is the initial volume, and ΔT is the change in temperature.

The minimum volume of the reservoir tank needed to hold the overflow of water is equal to the sum of the expansions of the water and the copper pipe.

To calculate the volume of the reservoir tank, we first need to calculate the change in volume of the water and the copper pipe separately. Then, we add these two volumes together to get the minimum volume of the reservoir tank.

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