What are the minimum and maximum temperatures?

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Homework Help Overview

The problem involves a 1-kg steel rod at 227°C being dropped into a 1-litre bath of water at 27°C, with the goal of determining the final temperature after thermal equilibrium. Participants are exploring the maximum and minimum temperatures the steel rod could reach in this scenario.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the concept of thermal equilibrium and the limits of temperature for the steel rod, questioning whether it can exceed the initial temperatures of the rod and water. There is also a discussion about the specific heat capacities of the materials involved and their potential variability.

Discussion Status

Some participants have provided guidance regarding the reasonable temperature limits for the rod, while others are questioning the assumptions made in the calculations, particularly regarding specific heat capacities and the implications of reaching temperatures above the boiling point of water.

Contextual Notes

There is a mention of the potential for water to boil off, which raises questions about whether this needs to be considered in the calculations. Additionally, participants note the variability in specific heat capacities for steel and water, suggesting that this could affect the problem's setup.

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Homework Statement



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. Homework 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!
[/B]
 
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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.
 
nasu said:
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.

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

Chet
 
None of the water boils off, no.
 
Dustin Cuocci said:
None of the water boils off, no.
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
 
I think I was using the wrong specific heat capacity numbers for both materials.
 

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