# Homework Help: What are the minimum and maximum temperatures?

1. Nov 5, 2014

### Dustin Cuocci

1. The problem statement, all variables and given/known data

A 1-kg steel rod is at 227C and is dropped into a 1-litre bath of water at 27C. Assume that these materials are thermally insulated from the rest of the universe. You will determine the final temperature of the steel rod after it reaches thermal equilibrium with the water.

A. Before you calculate this temperature, what are the maximum and minimum temperatures that the steel rod could be at after thermal equilibrium in this situation?

B. Determine the final temperature of the water after the two have reached thermal equilibrium.

2. Relevant equations
The Energy Principle:
Delta E = Wsurroundings

C is the specific heat capacity of each material.

3. The attempt at a solution

Delta Erod + Delta Ewater = 0
Crod*Mrod*Delta Trod = -Cwater*Mwater*Delta Twater
Crod*Mrod*(Tfrod-Tirod)=-Cwater*Mwater*(Tfwater-Tiwater)

Tfrod=Tfwater=Tf

(1.08)*(1000g)*(Tf-227)=-(1)*(1000g)*(Tf-27)
1080Tf-245160=-1000Tf+27000
2080Tf=272160
Tf=130.85C

Hopefully I've applied the principles and done the mathematics correctly, but I'm super confused about part A. I have no idea what the minimum and maximum temperatures for the rod could be. I guess they're the initial temperatures for both the rod and water - 227C and 27C but I don't know where to start. I'd appreciate any help you can provide. Thanks!

2. Nov 5, 2014

### nasu

I think you are right. The rod cannot be colder than 27 degrees or hotter than 227, can it?
So if you get a result of 400 degrees you know that something is wrong, don't you
It's good to know what will be a "reasonable" results before starting calculations.

3. Nov 5, 2014

### Dustin Cuocci

Thanks! I've come across several values for the specific heat capacity for steel and water though. Can someone recommend a dependable area that I can look it up?

4. Nov 5, 2014

### nasu

Well, the heat capacity depends on temperature. In the case of steel, it may depend on the specific composition. "Steel" is just a generic name.
But if it's just a textbook problem, it does not matter. If you have to solve a practical problem, you can look up your specific materials at the temperatures of interest.

5. Nov 5, 2014

### Staff: Mentor

Does any of the water evaporate (boil off), and, if so, do you need to take into account the heat of vaporization?

Chet

6. Nov 6, 2014

### Dustin Cuocci

None of the water boils off, no.

7. Nov 6, 2014

### Staff: Mentor

How do you know that? In your original post, you calculated a temperature of 130 C, which is above the boiling point of water.

Chet

8. Nov 7, 2014

### Dustin Cuocci

I think I was using the wrong specific heat capacity numbers for both materials.