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

1 Answer
Dec 16, 2016

Answer:

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.