An ice cube of mass 0.1kg at `0^@C` is placed in an isolated container which is at `227^@C`. The specific heat S of the container varies with temperature T according to the empirical relation `S=A+BT`, where `A=100 cal//kg-K and B=2xx10^-2cal//kg-K^2`. If the final temperature of the container is `27^@C`, determine the mass of the container. (Latent heat of fusion of water =`8xx10^4cal//kg`, Specific heat of water=`10^3cal//kg-K`).

Explanation

Heat received by ice is
`Q_(1)=mL+mC DeltaT=10700` cal
Heat given by the container is `Q_(2)`
`=-int_(500)^(300)m_(C)(A+BT)dT=-m_(C)[AT+(BT^(2))/2]_(300)^(300)=+21600m_(c)`
By principle of calorimetry `Q_(1)=Q_(2)`
`impliesm_(C)=0.495kg`