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It looks like your question got a little messed up when you entered it. I am guessing that the volume of water is 4 * 10^11 m^3.

A) Assuming that it is pure water at standard conditions.

The specific heat of water is c = 4.186 joule/gram °C

The density of water is p(density) = 1000 kg/m^3

Find the mass of water... V*p(density) = (4 * 10^11 m^3)*1000 kg/m^3 = 4*10^14 kg

Convert to grams = 4*10^14 kg * 1000 g/kg = 4*10^17 g

Q = c*m*T = (4.186 joule/gram C)*(4*10^17 g)*(10-8)

Q = 3.349*10^18 joules.

B) How many years...

1250 MW = 1250 MJ/sec = 1250*10^6 J/s = 1.25*10^9 J/s

Time = Q/E = (3.349*10^18 J)/(1.25*10^9 J/s) = 2.6792*10^9 seconds.

Convert to years...

Assuming 365.25 days in a year to account for leap year.

1 year = 31557600 seconds.

2.6792*10^9 seconds * 1year/31557600 seconds = 84.9 years.

Done.

1 m3 = 100 x 100 x 100 cu cm = 1,000,000 = 1x10^6 cu cm.

I'm not sure of your notation but just multiply the volume (in cu m) of Lake Erie by 1 x 10^6. That will give you the cu cm of Lake Erie. It takes one calorie to raise 1 cc one degree. So: If you are given that the vol of Lake Erie is 4 x 10^11. and the temp change = +2º C it would take 4 X 10^11 x 1 x 10^6 x 2.

It looks to me like 8x10^17 calories.

YOU convert it to joules, YOU determine the exhaust energy of the electric plant - and do the division.

Richard

(a) You could use the equation for Specific heat capacity. It is

Energy Transferred (J)= Mass(kg) * Specific heat capacity (J/Kg˚C) * Temperature change (˚C)

For this to work, you will have to convert the cubic meters into liters. 1 cubic meter is 1000 liters. Then you have to convert the liters into kilograms. With water, 1 liter is one kilogram, or 1000 grams.

The specific heat capacity of water is 4200 J/Kg˚C

The specific heat capacity means The energy needed to raise 1 kg of material by 1˚C.

I hope this helps. I have no answer to part (b), sorry.