# 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

Dec 16, 2016

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.