Water has a specific heat capacity of 4,186 J/kg °C. A tank contains 500 kg of water at 10.0 °C. The water is heated to a temperature of 90.0 °C. If electricity costs $0.100 per kilowatt-hour, then what is the cost of heating the water?

To solve this problem, we need to follow these steps:

1. First, we need to calculate the amount of energy required to heat the water. We can use the formula for heat energy which is Q = mcΔT, where m is the mass of the water, c is the specific heat capacity of the water, and ΔT is the change in temperature.

2. The mass of the water (m) is 500 kg, the specific heat capacity (c) is 4,186 J/kg °C, and the change in temperature (ΔT) is the final temperature minus the initial temperature, which is 90.0 °C - 10.0 °C = 80.0 °C.

3. Substituting these values into the formula gives us Q = 500 kg * 4,186 J/kg °C * 80.0 °C = 167,440,000 J.

4. However, the cost of electricity is given in kilowatt-hours, not joules. We need to convert joules to kilowatt-hours. There are 3,600,000 joules in a kilowatt-hour, so 167,440,000 J = 167,440,000/3,600,000 = 46.51 kWh.

5. Finally, we can calculate the cost of heating the water by multiplying the amount of energy used in kilowatt-hours by the cost per kilowatt-hour. So, the cost is 46.51 kWh * $0.100/kWh =$4.65.

So, the cost of heating the water is approximately $4.65.