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Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

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Heat and Temperature

1.How much ice should be added to "x" gram of water at "y" degree celsius to make the temperature "z" degree celsius? and WHY?
2.How much water of temperature "a" should be added to "x" gram of water at "y" degree celsius to make the temperature "z" degree celsius? and WHY?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

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Registered: 2010-06-20

Posts: 10,166

Re: Heat and Temperature

hi Agnishom,

How are you?  Haven't 'spoken' to you for a while.

So what's going to happen if you drop some ice into a beaker of water.  I'll assume there is enough water that's hot enough to melt it all, and that the ice is at zero degrees when it is dropped in. (If it comes straight from the freezer it will be colder!)

Firstly, the water will give up heat to melt the ice.  For that you need the 'latent heat' of fusion of water, which from Wiki is

Where Q is the heat required in Joules and m is the mass in g.

So let's say you need 'm' gms of ice.

Then

Then the heat of the x gms of water at y is going to shared equally by x + w gms of water to give a new temperature, z

Where C is the specific heat of water, Q the energy in Joules and T the temperature change in degrees Kelvin.

(Kelvin units of temperature are the same as Celcius, just with a different starting point.)

so

Assuming there are no heat losses elsewhere:

When I first posted an answer, it had an error, but this is the corrected version.  I got my wife, who is a science teacher, to check it and find my mistake. 

Question 2 is easier once you've struggled through this one, so maybe you'd like to try it yourself and post your answer.  You haven't got to worry about ice melting so it's just a case of heat given up by one, and gained by the other.

Bob

Last edited by Bob (2011-10-04 03:46:31)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Heat and Temperature

TNX
I am well
and
I think that in the second problem, there should be "334m+4.2m(z-a)" instead of "34m+4.2mz"

Last edited by Agnishom (2011-10-04 22:20:41)

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,166

Re: Heat and Temperature

hi Agnoshom,

For problem two, there is no ice so no melting required.  So drop the 344m term altogether.  Then you have it.

You'll find the 4.2 s cancel out.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob