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

[sap_54]

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

 

[Gamma]

1 b. Power = Energy / time.

 

[quicknote]

I can provide some guidance and clarification on these thermodynamics problems.

1.) For part A, you have correctly calculated the amount of heat required to raise the temperature of Lake Erie by 1 degree Celsius. To relate this to time, you can use the formula Q=mcΔT, where Q is the heat energy, m is the mass of the water, c is the specific heat capacity of water (4.186 J/g°C), and ΔT is the change in temperature. You can rearrange this formula to solve for time (t), which would be t=Q/(mcΔT). This will give you the amount of time required to supply the heat energy needed to raise the temperature of Lake Erie by 1 degree Celsius.

For part B, you need to consider the power output of the 1000-MW electric power plant. This power output is given in Watts (J/s), so you need to convert it to Joules per second (J/s). You can then use this value to calculate the amount of time required to supply the heat energy needed to raise the temperature of Lake Erie by 1 degree Celsius.

2.) Your equation is on the right track, but you need to consider the latent heat of fusion for the ice (334 J/g) since it is melting from a solid to a liquid. Also, the specific heat capacity for water is different for liquid (4.186 J/g°C) and solid (2.108 J/g°C) states. So, you will need to use the appropriate specific heat capacity for each state in your equation. Once you have solved for the final temperature, you can use the equation Q=mL to calculate the amount of ice melted, where m is the mass of the ice and L is the latent heat of fusion.

3.) In this problem, you are correct to use the equation Q=mcΔT to calculate the heat given off by the cooling liquid and the ideal gas. However, you also need to consider the work done by the expanding gas. The ideal gas law, PV=nRT, can be used to relate the initial and final volumes of the gas. You can rearrange this equation to solve for the initial volume (V initial) and then use it in your calculation for the work done by the gas (W=nRTln(V final/V initial)). This will give you the change in energy (ΔU) for the gas, which can