Final answer:
To determine the energy needed to change the temperature of Lake Erie's water, the specific heat capacity formula is applied; then to find out how long an electricity generating plant would take to supply that energy, conversion from megawatts to joules per second is used followed by a conversion of time from seconds to years.
Step-by-step explanation:
To calculate the energy required to increase the temperature of a volume of water in Lake Erie, we need to use the specific heat capacity formula: Q = mcΔT, where Q is the heat energy in joules, m is the mass in kilograms, c is the specific heat capacity of water (approximately 4.184 J/g°C), and ΔT is the change in temperature in Celsius. Since we are given the volume of water and the density of water is 1 g/mL at 20°C and 1 atm, we can convert volume to mass (since 1 mL of water at this condition has a mass of 1 gram) and then use this mass to calculate the energy required when the temperature changes from 15.8°C to 24.6°C.
For the second part, to calculate the time required by an electricity generating plant with an output of 1400 MW to supply this energy, we first need to convert megawatts to joules per second (since 1 MW = 1 million joules per second), and then divide the total energy required (in joules) by the plant's energy output rate (in joules per second) to find the time in seconds. Finally, we convert the time from seconds to years.