When water (at temperature
θ ) is mixed with ice (at
0∘ ), heat will flow from the warmer water to the ice.
The water cools down from
θ to
0∘C.
The ice melts, using that heat.
No heat is lost to surroundings.
Step 1: Heat lost by water cooling to
0∘CQ‌lost ‌=msθStep 2: Heat gained by ice (for melting)
If
x is the mass of ice melted, then:
Q‌gained ‌=xLStep 3: Equating heat lost and gained
msθ=xLStep 4: Solve for
xx=‌Step 5: Check if
M (the large mass of ice) matters
Since
M is very large, its temperature doesn't rise; it only partly melts.
Hence
M appears only to indicate that the ice remains at
0∘C.
Final Answer:
x=‌
