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For Part A, we can use the formula Q = mc(T'f - Ti) to calculate the energy required to raise the temperature of the water. Here, Q is the energy required, m is the mass of the water, c is the specific heat capacity of water at 20°C and 1 atm (4.184 J/g°C), T'f is the final temperature (21.6°C), and Ti is the initial temperature (11.2°C).
First, we need to find the mass of the water. Since density = mass/volume, we can rearrange the formula to get mass = density * volume. Plugging in the given values, we get:
mass = (998 kg/m^3) * (4.80 x 10^11 m^3) = 4.79 x 10^14 kg
Now, we can plug in the values into the formula above:
Q = (4.79 x 10^14 kg) (4.184 J/g°C) (21.6°C - 11.2°C) = 2.02 x 10^19 J
Therefore, it would require 2.02 x 10^19 J of energy to raise the temperature of Lake Erie from 11.2°C to 21.6°C.
For Part B, we can use the formula P = E/t to calculate the time required to supply the energy using a power of 1,400 MW. Here, P is the power in watts, E is the energy required in joules (which we found in Part A), and t is the time in seconds. Since we want the time in years, we can convert from seconds to years at the end by dividing by the number of seconds in a year (31,536,000 s).
First, we need to convert the power from MW to W:
P = 1,400 MW * (10^6 W/MW) = 1.4 x 10^9 W
Now, we can rearrange the formula to solve for t:
t = E / P = (2.02 x 10^19 J) / (1.4 x 10^9 W) = 1.44 x 10^10 s
Converting from seconds to years, we get:
t = 1.44 x 10^10 s / 31,536,000 s/year = 456.7 years (rounded to three significant figures)
Therefore, it would take approximately 457 years to supply the energy needed by using a power of 1,400 MW generated by an electric power plant.