Calculating the final temperature of a mixture when ice & water

In summary: Just remember to double check your calculations and units to make sure they are consistent. In summary, the conversation discusses how to calculate the final temperature of a mixture of ice and water, and the poster shares their attempted equation and asks for help. The expert provides a detailed breakdown of the calculations and points out some errors, ultimately confirming the correctness of the method.
  • #1
Jham808
7
0
Hello,

How do I calculate the following. The final temperature of a mixture of of ice and water. Where 176grams of ice at -10celsius mixes with 206 grams of water at 73.3celsius. I have tried this equation in multiple fashions and cannot seems to come to a consistent answer! Any help would be appreciated!

Why does the below not work?
water specific heat=4.184
ice specific heat= 2.11
heat of fusion=334

((specific Heat ice)X(Mass ice)x(∆temperature))+((mass ice)*(heat of fusion))+((specific Heat ice)X(Mass ice)x(x-0))=((specific Heat water)X(Mass water)x(∆temperature))

any help would be great appreciated

Additional Details
This is taking place in a completely insulated environment.
 
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  • #2
Try doing this in stages. How much heat is required to bring the ice to the point of melting? Does the water have that much heat in it? If it does, then how much heat is left? Is it enough to melt all the ice? And so on.
 
  • #3
Hello Voko,

I have tried this in stages but continue to do something incorrectly.

The Amount of Energy in Water
((specific Heat water)X(Mass water)x(∆temperature))
4.18 X 73.3C X 206gram=63,117Joules

The Amount of Energy to get ice to melting point
((specific Heat ice)X(Mass ice)x(∆temperature))
2.11 * 10c * 176grams=3,713Joules

Energy for Melting
((mass ice)*(heat of fusion))
334*176=58,784

Total Energy of ice melt and bringing to melting point
((specific Heat ice)X(Mass ice)x(∆temperature))+((mass ice)*(heat of fusion))
62,497

62,497<63,117 complete melting of ice occurs

the remaining energy is 602 joules
the total remaining water mass is 176+206=382grams
620joules=382grams * 4.18 * (x-0)
602= 1,597 * (x-0)
0.38=(x-0)

This does not seem correct though
 
Last edited:
  • #4
I get 620 J for the residual heat.
 
  • #5
Sorry 620 is the number that I come to. "602" was a typo. Is this the correct calculation?
 
  • #6
Jham808 said:
Sorry 620 is the number that I come to. "602" was a typo. Is this the correct calculation?

I do not see any error.
 
  • #7
voko said:
I do not see any error.

Actually, I do.

This: "176+206=326" can't be right.
 
  • #8
good catch I have corrected the 602 error and 326 error in my post. Other than those two Items, you believe my method is the exact way to calculate this problem?
 
  • #9
Everything else looks good.
 

Related to Calculating the final temperature of a mixture when ice & water

1. How do you calculate the final temperature of a mixture of ice and water?

In order to calculate the final temperature of a mixture of ice and water, you will need to use the formula Q = mCΔT, where Q is the heat gained or lost, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature. You will also need to take into account the latent heat of fusion for the ice, which is the amount of energy required to change the state of the ice from solid to liquid.

2. What is the specific heat capacity?

The specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is a physical property that is unique to each substance and is measured in units of joules per gram per degree Celsius (J/g°C).

3. How is the latent heat of fusion related to the final temperature of a mixture of ice and water?

The latent heat of fusion is the amount of energy required to change the state of a substance from solid to liquid, or vice versa, without a change in temperature. In the case of a mixture of ice and water, the heat gained by the ice as it melts (latent heat of fusion) will contribute to the final temperature of the mixture.

4. What is the difference between heat and temperature?

Heat is a form of energy that flows from a hotter object to a colder object. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in a substance. In the context of calculating the final temperature of a mixture of ice and water, heat is the energy gained or lost by the substances, while temperature is the resulting measurement of the average kinetic energy of the particles.

5. How does the mass of the substances affect the final temperature of the mixture?

The mass of the substances does play a role in calculating the final temperature of the mixture. The greater the mass, the more heat is required to raise the temperature of the substances. This means that a larger mass of ice will require more heat to melt and raise the temperature of the water, resulting in a lower final temperature compared to a smaller mass of ice and water.

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