Question

How much does approximately a cup of water increase in temperature when heated in a microwave for 45 seconds?

Answer 1

Answer:

32 K

Explanation:

A cup of water has a volume of approximately $236 \text{ cm}{}^3$. With water having a density of $1 \text{ g/cm}{}^3$, the mass of water in a cup is $1 \text{ g/cm}{}^3 \times 236 \text{ cm}{}^3 = 236\text{ g} = 0.236\text{ kg}$.

A microwave outputs about 700 W of power. In 45 seconds, the energy expended is $700 \text{ W} \times 45 \text{s} = 31500 \text { J}$.

The heat energy supplied to the water is related to the temperature change and the mass of the water by

$H = mc\Delta\theta$ where $c$ is the specific heat capacity of water. This value is $c = 4200 \text{ J/kg K}$.

$\Delta\theta$ is the temperature change.

$\Delta\theta = \dfrac{H}{mc}=\dfrac{31500}{0.236\times4200}=32 \text{ K}$