Final answer:
The rate of heat transfer to the pan is 2.59 kW.
Step-by-step explanation:
The rate of heat transfer to the pan can be calculated using the equation for heat transfer. The heat lost by the water is equal to the heat gained by the pan. Given that the water level in the pan drops by 10.2 cm in 45 min, we can calculate the mass of water evaporated using the volume of the pan. By using the properties of water at 79.5 kPa, we can find the heat transfer rate. The rate of heat transfer to the pan is 2.59 kW (kilowatts).