500 gms of water is to be cooled from `3.5^@C` to `20^@C` . How many grams of ice at `-10^@C` will be required for this purpose?
Specific heat of ice = `0.5 cal g^(-1) ""^@C^(-1)`
Latent heat of ice = `80 cal g^(-1)` ?

Explanation

To solve the problem of how many grams of ice at -10°C are required to cool 500 grams of water from 35°C to 20°C, we will use the principle of conservation of energy. The heat lost by the water will be equal to the heat gained by the ice.

### Step-by-Step Solution:

1. **Calculate the heat lost by the water (Q1)**:
The formula for heat lost or gained is given by:
\[
Q = mc\Delta T
...