Calorimeter Problem: Final Temp of Water & Ice Mixture

In summary, to find the final temperature of the mixture, we need to calculate the heat lost by the water as it cools to 0 C, the heat needed to melt the ice, and the heat gained by the aluminum calorimeter. Using the given values and equations, the final temperature is calculated to be 66.6 C.
  • #1
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Homework Statement


A 200.0 g aluminum calorimeter holds 300g of water at 75 C. 20 g of ice at 0 C are added to the water. What is the final temperature of the mixture?


Homework Equations


Use Lf= 33.5 x 104
Cal= 900 J/kg C

The answer is 66.5 C

The Attempt at a Solution


Don't know where to start.
 
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  • #2
Well, this is what i came to:

Find the heat lost by the water, if it is cooled to 0 C:
(.3)(4186)(75) = 94185

Calculate the heat needed to melt the ice:
(.02)(33.5e4) = 6700Q left:
( 94185 - 6700) = 87485

Final temp = 87485 / ( .32)(4186) = 65.3 C

The answer is 66.5 C. I don't know what to do with the aluminum
 
  • #3
Woohoo I think I got it:

QAL = (.2)(900)(65.3-75) = 1746

Final temp = (1746 + 87485) / (.32*4186) = 66.6 C
 

1. What is a calorimeter problem?

A calorimeter problem is a type of problem in which you are given the initial temperature and mass of two substances, usually water and ice, and asked to calculate the final temperature when they are mixed together.

2. How does a calorimeter work?

A calorimeter works by measuring the heat transfer between two substances. In a typical calorimeter, the two substances are separated by a barrier and the change in temperature of each substance is recorded. By knowing the specific heat capacity of each substance, the final temperature can be calculated.

3. What is specific heat capacity?

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 characteristic property of a substance and is measured in units of joules per gram per degree Celsius (J/g°C).

4. How do you calculate the final temperature in a calorimeter problem?

To calculate the final temperature, you can use the formula Q = mCΔT, where Q is the heat transferred, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature. By setting Q equal for both substances and solving for the final temperature, you can determine the final temperature of the mixture.

5. What are some sources of error in a calorimeter problem?

Some sources of error in a calorimeter problem include heat loss to the surroundings, incomplete mixing of the substances, and inaccuracies in the measurements of mass and temperature. It is important to minimize these sources of error in order to obtain a more accurate result.

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