Melting snow for drinking water: sensible heat, then latent heat
SNC2D Grade 10 Science · Climate Change
On a February trip in Algonquin Park a camper scoops 1.50 kg of snow at −12.0 °C into a pot and sets it on a stove that delivers 1200 W of heat into the pot. Taking the specific heat capacity of ice as 2100 J/(kg·K) and the latent heat of fusion as 334 kJ/kg, find the heat needed to bring the snow up to 0 °C and how long that takes, then the heat needed to melt it and how long <em>that</em> takes.
Nothing can melt until the snow reaches 0 °C, so the temperature climb is the first bill to pay. ΔT is a difference, so −12.0 °C to 0 °C is 12.0 K.
Carried onward at full precision, not this rounded figure.
The stove delivers joules at a steady rate, so that heat divided by 1200 W is the time on the clock.
Carried onward at full precision, not this rounded figure.
Now the phase change. There is no ΔT in this formula at all — the thermometer sits at 0 °C the entire time the ice is disappearing.
Carried onward at full precision, not this rounded figure.
Same stove, same arithmetic as step 2 — and an answer more than thirteen times longer. That gap is the lesson.
Carried onward at full precision, not this rounded figure.
Why this order
The chain is split into two heat calculations because they are two genuinely different physical processes, and the classic mistake is to run them together with one Q = mcΔT from −12 °C to some final temperature. That is wrong twice over: it ignores the 501 kJ the melting itself demands, and it uses ice's specific heat for water that no longer exists. Steps 1 and 3 have to be separate lines on the page, and the times in steps 2 and 4 show why anyone should care — 31.5 s to warm the snow, 417.5 s to melt it. Almost seven minutes of a stove's fuel goes into a phase change that the thermometer refuses to acknowledge.
This is also the arithmetic behind spring breakup and behind why Canadian lakes lag the calendar. A lake that has finally reached 0 °C still has to absorb 334 kJ for every kilogram of ice before open water appears, which is why ice can persist through weeks of above-zero air. The same latent heat runs in reverse in the fall: freezing releases it, which is why a large lake holds the first frost off its own shoreline. Joseph Black measured exactly this in Glasgow in the 1760s, and it remains the single largest term in any honest energy budget for a melting ice sheet.
Carried values move at full precision, not the rounded figure shown — chaining rounded numbers compounds error.