Question
g of ice at C is mixed with g of water at C in an insulated container. Find the final temperature. Use cal/g·°C, cal/g·°C, latent heat of fusion cal/g.
Solution — Step by Step
Heat to warm ice from to C: cal.
Heat to melt ice at C: cal.
Total to bring ice to C water: cal.
Heat released by g water cooling from to C: cal.
Since , all the ice melts and we still have cal of “leftover” heat.
The melted ice is now g of water at C, joining the g already cooled to some temperature. Total water mass = g. Let final temperature be .
Heat balance from the equilibrium state: the leftover cal warms g from C:
Final answer: C.
Why This Works
Calorimetry is bookkeeping: heat lost by hot stuff equals heat gained by cold stuff (in an insulated system). The catch is that “heat gained” includes warming, melting, vaporising, and cooling — each with its own formula.
The “check whether all the ice melts” step is non-negotiable. If the warm water cannot supply enough heat for the full melt, the final temperature stays at C with some ice unmelted.
Alternative Method
Set up the equation in one shot. Let be the final temperature (assume all ice melts). Heat gained by ice = . Heat lost by water = . Equate:
, giving , C. Same answer.
Always do the “is there enough heat?” check before assuming a uniform final temperature. NEET loves to set g ice with g water and trick you into a positive when the answer is actually C with partial ice remaining.
Common Mistake
Forgetting the latent heat term. Students compute only the warming heat and end up with a wildly wrong answer. The phase change at C is usually the largest single term — never skip it.