Lake Erie contains roughly 4.00 times 10^11 m^3 of water. How much energy is req
ID: 1409453 • Letter: L
Question
Lake Erie contains roughly 4.00 times 10^11 m^3 of water. How much energy is required to raise the temperature of that volume of water from 17.4 degree C to 23.0 degree c?(Assume the density of this water to be equal to that o water at 20 degree C and 1 atm.) How many years would it take to supply this amount of energy by using the 1, 200-MW exhaust energy of an electric power plant? An aluminum rod it 22.5 cm long at 20 degree C and has a mass of 350 g If 11,000 of energy is added to the rod by neat, what It the change in length of the rod? (The average coefficient of linear expansion for aluminum it 24 times 10^-6 (degree c)^-1)Explanation / Answer
a)
for the water Q = m * c * delta T
the volume V of the water is given , the mass m is required
density is defined p = m / V
so , m = p * V = 1 * 10^3 kg/m^3 * 4 * 10^11 m^3
m = 4 * 10^14 kg
hence
Q = m * c * delta T
Q = 4 * 10^14 kg * 4.186 * 10^3 * ( 23 - 17.4)
Q = 9.37 * 10^18 J
b)
power = energy / time
t = Q / power
t = ( 9.37 * 10^18) / (1200 * 10^6)
t = 7.8 * 10^9 J/s
then
= (7.8 * 10^9 sec ) / ( 3.156 * 10^7 sec/year)
= 247.14 years
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