How long will a 1 kilo-Watt electric kettle take to heat 1000gm of water from 20 degrees C 80 C?

- Power of electric kettle, $P = 1 \text{ kW} = 1000 \text{ W}$

- Mass of water, $m = 1000 \text{ gm} = 1 \text{ kg}$

- Initial temperature of water, $T_i = 20°\text{C}$

- Final temperature of water, $T_f = 80°\text{C}$

- Specific heat capacity of water, $c_w = 4.18 \text{ J/g}°\text{C}$

To find:

- Time taken to heat water, $t$

The energy required to raise the temperature of the water from $T_i$ to $T_f$ is given by:

$$Q = mc_w (T_f - T_i)$$

Substituting the given values, we get:

$$Q = (1 \text{ kg})(4.18 \text{ J/g}°\text{C})(80°\text{C} - 20°\text{C})$$

$$Q = 2508 \text{ J}$$

The power of the electric kettle is the rate at which it can supply energy. So, the time taken to heat the water can be calculated as:

$$t = \frac{Q}{P}$$

Substituting the values of $Q$ and $P$, we get:

$$t = \frac{2508 \text{ J}}{1000 \text{ W}}$$

$$t \approx 2.51 \text{ s}$$

Therefore, the 1 kilo-Watt electric kettle will take approximately 2.51 seconds to heat 1000gm of water from 20 degrees C to 80 degrees C.