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Let the resultant temperature be
Use to find heat lost when steam at 100°C condenses to water at 100°C
Use to find heat lost when water 100°C cools to
Add 2 and 3 to final total heat lost.
Use to find heat gained when ice at 0°C melts to form water at 0°C.
Use to find heat gained when water at 0°C to θ°C.
Add 5 and 6 to find total heat gained.
Equate 4 and 7 to find in the given form.