Answer:
32 K
Explanation:
A cup of water has a volume of approximately [tex]236 \text{ cm}{}^3[/tex]. With water having a density of [tex]1 \text{ g/cm}{}^3[/tex], the mass of water in a cup is [tex]1 \text{ g/cm}{}^3 \times 236 \text{ cm}{}^3 = 236\text{ g} = 0.236\text{ kg}[/tex].
A microwave outputs about 700 W of power. In 45 seconds, the energy expended is [tex]700 \text{ W} \times 45 \text{s} = 31500 \text { J}[/tex].
The heat energy supplied to the water is related to the temperature change and the mass of the water by
[tex]H = mc\Delta\theta[/tex] where [tex]c[/tex] is the specific heat capacity of water. This value is [tex]c = 4200 \text{ J/kg K}[/tex].
[tex]\Delta\theta[/tex] is the temperature change.
[tex]\Delta\theta = \dfrac{H}{mc}=\dfrac{31500}{0.236\times4200}=32 \text{ K}[/tex]
