An electric heater of power 150 W is immersed in 0.75 kg of ice at `0^@`C in a lagged container of negligible heat capacity. The temperature remains constant for 27-5 minutes and then rises to `40-0^@`C in a further 14 minutes. Explain why does the temperature remain constant. Calculate : (a) the specific latent heat of ice, and (b) the specific heat capacity of water.

Explanation

To solve the problem step by step, we will first explain why the temperature remains constant, and then we will calculate the specific latent heat of ice and the specific heat capacity of water.

### Step 1: Explain why the temperature remains constant
When the electric heater is turned on, it supplies heat to the ice. However, during the melting process, the temperature of the ice-water mixture remains constant at 0°C until all the ice has melted. This is because the heat energy supplied by the heater is used to change the state of the ice from solid to liquid (melting) rather than increasing the temperature. The energy required for this phase change is known as the latent heat of fusion.

### Step 2: Calculate the heat energy supplied by the heater during the first 27.5 minutes
The power of the heater is given as 150 W (watts), which is equivalent to 150 joules per second.

...