Question

A 10-lane Olympic-sized swimming pool contains `2 x 10^6` kg of water. If the water is at 0°C, how many kilojoules of energy must be removed to freeze the water in this pool? `DeltaH_(fus)` for `H_2O` = 334 J/g

Answer 1

You must remove `7 ×10^8color(white)(l) "kJ"` of energy.

Explanation:

The opposite of "enthalpy of fusion" is enthalpy of solidification, `Δ_"sol"H`.

`Δ_"sol"H = "-"Δ_text(fus)H`

The energy `q` that must be removed in freezing a mass `m` of a liquid is

`color(blue)(bar(ul(|color(white)(a/a) q = mΔ_"sol"Hcolor(white)(a/a)|)))" "`

The energy involved in freezing the pool is

`q = 2 × 10^6 color(red)(cancel(color(black)("kg"))) × (1000 color(red)(cancel(color(black)("g"))))/(1 color(red)(cancel(color(black)("kg")))) × ("-334" color(red)(cancel(color(black)("J"))))/(1 color(red)(cancel(color(black)("g")))) × "1 kJ"/(1000 color(red)(cancel(color(black)("J")))) = "-7" × 10^8 color(white)(l)"kJ"`

Thus, you must remove `7 × 10^8color(white)(l) "kJ"` of energy.