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 cc of water at `27^(@)`C. The final temperature is `40^(@)`C. Calcualte the specific heat of the metal. If heat losses to the surroundings are not negligible, is our answer greater or smaller than the actual value of specific heat of the metal?

Explanation

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)`