The mechanical Equivalent of heat: total increase in temperature of the water?

In summary, the conversation discusses a problem involving Joule's paddle wheel experiment with a falling block and a body of water. They solve for potential energy and thermal energy, and discuss the relationship between the two. They also mention the concept of conservation of energy and define the symbol J as the unit joule of energy.
  • #1
lalahelp
75
0

Homework Statement


If in Joule's paddle wheel experiment a block of mass 10 kg is allowed to fall through 22.5 meters and the mass of the water is 50 grams. What is the total increase in temperature of the water?



Can your value of J be used for determining how much mechanical energy can be produced from a specified amount of thermal energy?

Homework Equations


Im not sure how to start the problems and do not know what to do could someone please help and explain them to me
 
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  • #2
What's the formula for potential energy (something with mass and height in it)?
And for thermal energy (something with mass and temperature in it)?
 
  • #3
PE=mgh
Thermal energy= mct

what do I do from there?
 
  • #4
Good! :smile:

lalahelp said:
PE=mgh

What would m be in this problem?
And g?
And h?

lalahelp said:
Thermal energy= mct

What would m be in this context?
Do you have a value for c?
How does t fit into your problem?
 
  • #5
m=10 kg
g=9.8 m/s^2
h=22.5 m
___________
m=50 g
c=4185.8 kg c
t= I am not sure...
 
  • #6
Right!

Now there is something called conservation of energy.
When your block falls, its potential energy has to go somewhere.
It is converted into heat.
What do you think the relation would be between the potential energy and the thermal energy?

As for "t".
What is it exactly that the problem asks you to calculate?
 
  • #7
the potential energy equals the thermal energy?
the problem is asking for the total increase in temperature...
 
  • #8
lalahelp said:
the potential energy equals the thermal energy?

Exactly!

lalahelp said:
the problem is asking for the total increase in temperature...

Yes. And "t" is the symbol for the change in temperature.

So...?
 
  • #9
ohhh ok i got it Thank you!
could you explain the second question now lol your very helpful
 
  • #10
What is J?
And what are your thoughts on it?
 
  • #11
J is mgh/mct

My book does not say anything about it, it just gives an equation so I am not sure...
 
  • #12
Okay, so you can calculate J, can't you?

Can you put into words what J signifies?
 
  • #13
J means Joules... I thought it was only a unit...
 
  • #14
Yes, J is usually the unit joule of energy.
That's why I asked, because the way J is used in your problem description suggests that J is used for something else...?
Where did your formula for J come from?
 
  • #15
My physics book... its a conceputal problem. Yeh I was confused because it didnt say where that came from.
 
  • #16
Conceptual problem or not, symbols always need to be defined before you can talk about concepts.
Is it defined as the formula you gave then?
 
  • #17
My book says that's how you solve for J, so yes.
 
  • #18
Can you put into words what the formula means then?
 
  • #19
Yes it is defined as the formula
 
  • #20
So what's in the nominator of the formula? And what's in the denominator?
Do you recognize those?
 

1. What is the mechanical equivalent of heat?

The mechanical equivalent of heat is the amount of mechanical energy needed to produce a unit of heat energy, or the amount of heat energy that can be produced by a unit of mechanical energy.

2. How is the mechanical equivalent of heat determined?

The mechanical equivalent of heat is typically determined through experiments using a device called a calorimeter, which measures the amount of heat produced by a known amount of mechanical energy. This value is then compared to the measured increase in temperature of a known amount of water.

3. What is the relationship between mechanical energy and heat energy?

The mechanical equivalent of heat is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another. Therefore, mechanical energy and heat energy are directly related and can be converted into each other.

4. How is the mechanical equivalent of heat used in practical applications?

The mechanical equivalent of heat is an important concept in many areas of science and engineering, including thermodynamics and energy conversion. It is used to understand and predict the behavior of various systems and to design efficient machines and processes.

5. Why is the mechanical equivalent of heat important?

The mechanical equivalent of heat is important because it helps us understand the relationship between mechanical and heat energy, and how they can be converted into each other. This knowledge has many practical and theoretical applications in various fields and is crucial for our understanding of the fundamental laws of nature.

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