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

To solve the problem, we will follow these steps:

### Step 1: Understand the heat transfer process
We have an ice cube at 0°C placed in a container at 227°C. The ice will absorb heat and melt, while the container will lose heat. The final temperature of both the ice (now water) and the container will be 27°C.

### Step 2: Calculate the heat gained by the ice
The heat gained by the ice consists of two parts:
1. The heat required to raise the temperature of the ice from 0°C to 27°C.
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