Question

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 17.8°C to 21.6°C? (Assume the density of this water to be equal to that of water at 20°C and 1 atm.) J (b) How many years would it take to supply this amount of energy by using the 1,400-MW exhaust energy of an electric power plant? yr

Answer 1

Answer:

Part a)

$Q = 6.36 \times 10^{18} J$

Part b)

$t = 144.11 years$

Explanation:

Part a)

Energy required to raise the temperature of water from 17.8 degree C to 21.6 degree C is given by formula

$Q = ms\Delta T$

here we know that

Here the volume of the water is given as

$V = 4.00 \times 10^{11} m^3$

now the mass of water is

$m = density \times volume$

$m = 4.00 \times 10^{14} kg$

now the heat required is

$Q = (4 \times 10^{14})(4186)(21.6 - 17.8)$

$Q = 6.36 \times 10^{18} J$

Part b)

As we know that power is supplied at

$P = 1400 MW$

so here we know

$P = \frac{Q}{t}$

so here we have

$t = \frac{Q}{P}$

$t = \frac{6.36 \times 10^{18}}{1400 \times 10^6}$

$t = 4.54 \times 10^9 s$

$t = 144.11 years$