A piece of ice of mass 0.08 kg, at 0 °C, is dropped into 0.4 kg of lemonade at 30 °C.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A piece of ice of mass , at , is dropped into of lemonade at . Treat the lemonade as water. Find the final temperature when all the ice has melted. Use to melt ice, and for water.
Need a reminder? The key ideaShow
During a change of state the temperature stays the same while heat goes in or comes out: the latent heat. , with to melt ice and to boil water. To warm water, .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Heat given out by the lemonade. .
Step 2. Heat taken in. Melting: . Warming the melted ice: .
Step 3. Equal heats. , so , and .
Answer: .
Check. The ice is a fifth of the mass of the drink, so a big drop in temperature, but not down to , is sensible.
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