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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

Respuesta :

Answer:

Part a)

[tex]Q = 6.36 \times 10^{18} J[/tex]

Part b)

[tex]t = 144.11 years[/tex]

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

[tex]Q = ms\Delta T[/tex]

here we know that

Here the volume of the water is given as

[tex]V = 4.00 \times 10^{11} m^3[/tex]

now the mass of water is

[tex]m = density \times volume[/tex]

[tex]m = 4.00 \times 10^{14} kg[/tex]

now the heat required is

[tex]Q = (4 \times 10^{14})(4186)(21.6 - 17.8)[/tex]

[tex]Q = 6.36 \times 10^{18} J[/tex]

Part b)

As we know that power is supplied at

[tex]P = 1400 MW[/tex]

so here we know

[tex]P = \frac{Q}{t}[/tex]

so here we have

[tex]t = \frac{Q}{P}[/tex]

[tex]t = \frac{6.36 \times 10^{18}}{1400 \times 10^6}[/tex]

[tex]t = 4.54 \times 10^9 s[/tex]

[tex]t = 144.11 years[/tex]

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