Energy Transfer in a Water and Aluminum Pan System

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In summary, the temperature of the water and pan increased from 24° C to 74.6° C due to energy transfer from the electric stove into the system consisting of the water plus the pan.
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rkjul
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Homework Statement



100 grams of boiling water (temperature 100° C, heat capacity 4.2 J/gram/K) are poured into an aluminum pan whose mass is 375 grams and initial temperature 24° C (the heat capacity of aluminum is 0.9 J/gram/K).
(a) After a short time, what is the temperature of the water?

(b) Next you place the pan on a hot electric stove. While the stove is heating the pan, you use a beater to stir the water, doing 1400 J of work, and the temperature of the water and pan increases to 74.6° C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?


Homework Equations



deltaE=mC*deltaT
deltaE=Q+W

The Attempt at a Solution



Ok I got part A with no trouble but I'm struggling with part B. I tried using the mC*delta T equation for the water and the aluminum pan...adding those values and setting it equal to Q+W. I used 8.6 for delta T (74.6-66) since I got 66 degrees for my answer in part A. I then subtracted W to find Q in the second equation but it's not the correct answer. I think what might be throwing me is that the system consists of the water and pan. Any suggestions?
 
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  • #2
You didn't say what value of C you used in the second calculation. But C' should be the weighted average of the mass of the water and the aluminium ( British spelling), and M' the sum of the masses.

C' = (C1*M1 + C2*M2)/(M1+M2)
M' = M1 + M2.

I think this will work, but I could be wrong.
 
  • #3
Mentz114 said:
You didn't say what value of C you used in the second calculation. But C' should be the weighted average of the mass of the water and the aluminium ( British spelling), and M' the sum of the masses.

C' = (C1*M1 + C2*M2)/(M1+M2)
M' = M1 + M2.

I think this will work, but I could be wrong.

I calculated two values of mC*delta T, one for the water (100*4.2*8.6) and one for aluminum (375*0.9*8.6) and added those together and set that equal to Q+1400. I got Q=5115 (same answer as you) and it's incorrect.
 
  • #4
how did u get a?
 

FAQ: Energy Transfer in a Water and Aluminum Pan System

What is heat capacity and how is it measured?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius. It is measured in units of joules per degree Celsius (J/C). To measure heat capacity, the substance is heated and the change in temperature is recorded. Then, the amount of heat energy used is divided by the temperature change to determine the heat capacity.

How does heat capacity affect energy transfer?

The higher the heat capacity of a substance, the more heat energy it can store. This means that it will take longer for the substance to heat up or cool down compared to a substance with a lower heat capacity. Therefore, heat capacity affects the rate of energy transfer, with substances with higher heat capacities requiring more energy to change temperature.

Can heat capacity vary for different substances?

Yes, heat capacity can vary for different substances. It is dependent on the physical properties of the substance, such as its mass, temperature, and molecular structure. For example, substances with a higher number of molecules will have a higher heat capacity compared to substances with fewer molecules.

How is heat capacity related to specific heat?

Specific heat is the amount of heat energy required to raise the temperature of 1 gram of a substance by 1 degree Celsius. Heat capacity, on the other hand, is the amount of heat energy required to raise the temperature of any amount of a substance by 1 degree Celsius. The two are related by the mass of the substance, with specific heat being the heat capacity per unit mass.

What are some real-life applications of heat capacity and energy transfer?

Heat capacity and energy transfer play a crucial role in various everyday applications. For example, the heat capacity of water helps regulate the Earth's temperature, making it suitable for life. In cooking, understanding heat capacity and energy transfer is essential for controlling the temperature of food. In industries, heat capacity and energy transfer are used in processes such as heating and cooling, insulation, and refrigeration. Additionally, understanding these concepts is crucial in designing energy-efficient buildings and transportation systems.

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