Question
A 50 g ice cube at is dropped into 200 g of water at in an insulated cup. Find the final temperature. (, specific heat of water .)
Solution — Step by Step
Since , all ice melts and we still have leftover heat to warm the mixture.
After melting, we have 250 g of water (50 g from ice at + 200 g at some intermediate temp). Heat balance:
Final answer:
Why This Works
Calorimetry is bookkeeping: heat lost by hot stuff = heat gained by cold stuff. The trick with phase changes is checking whether the cold body has enough mass to absorb all the available heat for melting. If not, only part melts and the answer is 0°C.
Always do the “is there enough heat to melt all of it?” check first — saves you from setting up the wrong equation.
Alternative Method
Set the final temperature symbolically and write in one line. Same answer, but the partial-melt check still has to happen first.
Common Mistake
Students forget to warm the melted ice from to the final temperature. The 50 g of “ice water” needs calories — without that term, you get instead of .
If , the answer is automatically with some unmelted ice remaining. Don’t bother solving the heat-balance equation in that case.