# Thermodynamics - how much heat needed to raise temperature of a lake

I am working on my thermodynamics problems and I ran into a few problems on a couple of the questions:

1.) Lake Erie contains roughly 4.00*10^11 m^3 of water. (a) How much heat is required to raise the temperature of that volume of water from 11 degrees C to 12 degrees C? (b) Approxiamtely how many years would it take to supply this amount of heat by using the full output of a 1000-MW electric power plant?

*I got part A of the problem to be 1.67*10^18 J. I got really confused on part B; however, because I couldn't figure out how to relate this problem to time...

2.) Steam at 100 degress C is added to ice at 0 degrees C. Find the amount of ice melted and the final temperature when the mass of steam is 10 g and the mass of ice is 50 g.

*My equation was: (mass of steam)(Latent heat of vaporization)+(mass of steam)(specific heat of water)(T final-T initial)=(mass of ice)(Latent heat of vaporization)+(mass of ice)(specific heat of water)(T final-T initial)

I don't think this is right, though...

3.) One mole of water vapor at a temperature of 373 K cools down to 283 K. The heat given off by the cooling liquid is absorbed by 10 mol of an ideal gas, causing it to expand at a constant temperature of 273 K. If the final colume of the ideal gas is 20 L, determine the initial volume of the ideal gas.

*I used Q=mc(T final-T initial)
Found Q to = -180.9
and change in U=0 which means that the change in W= change in Q

Even though I found Q, I don't know how to find the change in Q, but someplace in this problem I think you need to use W=nRT(V final/V initial)

Any help would be greatly appreciated!
Thanks:rofl:

## Answers and Replies

1 b. Power = Energy / time.