A microwave oven works at 2.45 GHz. A cup holds 0.250 kg of water at 20 °C…

Step 1. The heat. $Q = mc\Delta T = 0.250\ \text{kg} \times 4186\ \text{J/(kg K)} \times 65\ \text{K} = 68.0\ \text{kJ}$.

Step 2. The time. We want $t$, so $t = \dfrac{Q}{P} = \dfrac{68023\ \text{J}}{560\ \text{W}} = 121\ \text{s}$. That is about two minutes.

Step 3. One photon. $E = hf = 6.63 \times 10^{-34}\ \text{J s} \times 2.45 \times 10^{9}\ \text{Hz} = 1.62 \times 10^{-24}\ \text{J}$.

Step 4. The number of photons. $N = \dfrac{Q}{E} = \dfrac{68023\ \text{J}}{1.62 \times 10^{-24}\ \text{J}} = 4.19 \times 10^{28}$.