Define (i) power, (ii) specific heat capacity - Leaving Cert Physics - Question 12 - 2006

Specific heat capacity is the amount of energy required to raise the temperature of 1 kg of a substance by 1 K (or 1 °C), and it is denoted as:

$c = \frac{Q}{m \Delta T}$

where Q is the heat energy in joules, m is mass in kilograms, and ΔT is the change in temperature in Kelvin.

To calculate the energy required to raise the temperature of the water from 15 °C to 100 °C, we use the formula:

$Q = mc \Delta T$

where:

• m = 0.4 kg (mass of water),
• c = 4200 J/kg K (specific heat capacity of water),
• \Delta T = (100 - 15) °C = 85 K.

Thus, we have:

$Q = 0.4 \times 4200 \times 85$

Calculating this gives:

$Q = 142800 J$

The energy supplied by the kettle per second can be calculated using its power rating:

$P = 3.0 kW = 3000 W$

Thus, the energy supplied per second is:

$E = P \cdot t = 3000 J/s$

Using the energy required and the power of the kettle, the least time taken can be calculated by:

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

Substituting the earlier computed values:

$t = \frac{142800 J}{3000 W} \approx 47.6 seconds$

In reality, the time taken to heat the water will be greater because some energy will be lost to the surroundings. This energy loss can be through heat escaping from the kettle or being absorbed by the kettle itself, as well as other factors like inefficiencies in the electric kettle.