Lake Erie contains roughly 4.00 1011 m3 of water.
(a) How much energy is required to raise the temperature of that volume of water from 9.0°C to 12.0°C?
(b) How many years would it take to supply this amount of energy by using the 850-MW exhaust energy of an electric power plant?
1.5 x 1018
To calculate the energy required to raise the temperature of a given volume of water, you can use the formula:
Q = mcΔT
where:
Q is the energy
m is the mass of water
c is the specific heat capacity of water
ΔT is the change in temperature
(a) To calculate the energy required to raise the temperature of 4.00 * 10^11 m^3 of water from 9.0°C to 12.0°C, we need to know the mass of the water. We can calculate the mass using the formula:
mass = volume * density
The density of water is approximately 1000 kg/m^3, so:
mass = 4.00 * 10^11 m^3 * 1000 kg/m^3
Now we can calculate the energy:
Q = mass * c * ΔT
The specific heat capacity of water, c, is approximately 4.18 J/g°C (or 4186 J/kg°C).
Substituting the values into the formula, we get:
Q = (4.00 * 10^11 m^3 * 1000 kg/m^3) * 4186 J/kg°C * (12.0°C - 9.0°C)
Simplifying the expression gives us the energy required to raise the temperature.
(b) To calculate the number of years it would take to supply this amount of energy using a power plant with an exhaust energy of 850 MW, we need to convert the energy required into joules per second (Watts).
The energy required is calculated in (a), and we'll denote it as E.
1 MW = 10^6 W
So, the exhaust energy of the power plant is 850 * 10^6 W.
The number of seconds in 1 year is 31,536,000 seconds (considering a non-leap year).
Now, we can calculate the number of years it would take:
Number of years = E / (exhaust energy of power plant (in Watts) * number of seconds in a year)
Substituting the values and calculating the expression will give you the number of years required to supply this amount of energy using the power plant.