An ice cube of mass 0.1 kg 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 = 2xx 10^-2 cal//kg.K^2`. If the final temperature of the container is `27^@C`, determine the mass of the container.
(Latent heat of fusion for water = `8xx 10^4 cal//kg`, specific heat of water `=10^3 cal//kg.K`).

Explanation

Container:
Initial temp: `T_1=227+273=500K`
Final temp: `T_2=27+273=300K`
Specific heat of container: `S=A+BT=100+2xx10^-2T`
Let `m:` mass of container
Heat lost by container
`DeltaQ=underset(T_(1))overset(T_(2))(int)mSdT=m underset(500)overset(300)(int)(100+2xx10^-2T)dT`