A piece of ice of mass 40g is added to 200g of water at 500C. Calculate the final temperature of water when all the ice has melted. Specific heat capacity of water =4200Jkg−1K−1 and specific latent heat of fusion of ice =336×103Jkg−1.
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Solution
Let final temperature of water when all the ice has melted = T°C.
Amount of heat lost when 200g of water at 50°C cools to T°C =200 ×4.2 ×(50 − T) = 42000 − 840T
Amount of heat gained when 40g of ice at 0oC converts into water at 0°C.= 40 ×336J = 13440 J
Amount of heat gained when temperature of 40g of water at 0°C rises to T°C = 40 ×4.2 ×(T-0) = 168T
We know thatAmount of heat gained = amount of heat energy lost.