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In an experiment on the specific heat of...

In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at `150^(@)C` is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing 150 cm3 of water at `27^(@)C`. The final temperature is `40^(@)C`. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value for specific heat of the metal ?

Text Solution

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Mass of water `(m_(1))=150g=0.15g`
Mass of metal `(m_(2))=0.20kg`
Water equivalent of calorimeter `W=0.025kg`
`t_(1)=27^(@)C,t_(2)=150^(@)C,t=40^(@)C,s_(1)=4.2xx10^(3)Jkg^(-1)K^(-1)`
Heat gaind by water and calorimeter `=(m_(1)+w)xxs_(1)xx(t-t_(1))`
`=(0.15+0.025)xx4.2xx10^(3)xx(40-27)=9.555xx10^(3)J`
Heat lost by meal `=m_(2)xxsxx(t_(2)-t)=0.20xxsxx(150-40)=22sJ`, where s is the specific heat of metal.
Equating 1 and 2 we have
`s=0.43xx10^(3)Jkg^(-1)K^(-1)`
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