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Question

A metal ball of mass 400g and at 600oC is placed on the block of ice, when 428g of ice melts. If the sp. heat capacity of metal ball is 0.6J g1oC1. Calculate sp. latent heat of ice.

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Solution

Given: A metal ball of mass 400g and at 600oC is placed on the block of ice, when 428g of ice melts. If the specific heat capacity of metal ball is 0.6J/(goC)
To find the specific latent heat of ice.
Solution:
As per the given criteria,
Mass of the metal ball, mb=400g
Temperature of the metal ball, Tb=600C
Mass of melted ice, mi=428g
Specific heat of metal ball, cb=0.6J/(goC)
As the block does not melt completely therefore final temperature is zero degree Celsius.
Heat gained by ice to melt =miL=428×L
Heat lost by metal ball =mbcbTb=400×0.6×600=144000J
We know,
Heat gained = heat lost
Therefore, 428×L=144000L=144000428=336.4J/g
is the specific latent heat of ice.

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