What is the final temperature of the mixture?

In summary, the final temperature of the mixture can be found by setting the heating and cooling ratios in the equation (1.1)(880)(92-t) = (0.5)(4200)(t-12) and solving for t. However, in the given attempt at a solution, an arithmetic mistake was made which resulted in an incorrect final temperature. It is important to always check for arithmetic errors when solving equations.
  • #1
Byeongok
13
0

Homework Statement


In an experiment, 1.1kg of aluminium is heated to 92 degrees Celsius it is then dropped into 0.5kg of water at 12 degrees celsius.

Find the final temperature of the mixture. (Cw= 4200JKg-1Celsius-1) (Cal= 880JKg-1Celsius-1)

Homework Equations


Qal = Qw

The Attempt at a Solution


(1.1)(880)(92-t) = (0.5)(4200)(t-12)
968( 92 - t ) = 2100( t - 12 )
89056-968t = 2100t - 25200
63856 = 3068t
20.81 = t
 
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  • #2
No.

As you suspected, I suppose.

You can check your answers yourself: if you put back "t=20.81" in the first line of your equation, you will see that you are way off.
From your second line, one can see that cooling and heating have a ratio of about 2:1 in temperature.
 
Last edited:
  • #3
Byeongok said:

Homework Statement


In an experiment, 1.1kg of aluminium is heated to 92 degrees Celsius it is then dropped into 0.5kg of water at 12 degrees celsius.

Find the final temperature of the mixture. (Cw= 4200JKg-1Celsius-1) (Cal= 880JKg-1Celsius-1)

Homework Equations


Qal = Qw

The Attempt at a Solution


(1.1)(880)(92-t) = (0.5)(4200)(t-12)
968( 92 - t ) = 2100( t - 12 )
89056-968t = 2100t - 25200
63856 = 3068t
Your problem lies in the arithmetic used to get the line immediately above.

Always check your work for arithmetic mistakes.
 

1. What is thermodynamics?

Thermodynamics is a branch of physics that deals with the relationships between heat, energy, and work. It is concerned with the behavior of matter and energy within a system, and how they change and interact with each other.

2. What are the laws of thermodynamics?

The four laws of thermodynamics are:
1) The first law: Conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted.
2) The second law: Entropy always increases in an isolated system, meaning that systems tend to become more disordered over time.
3) The third law: As temperature approaches absolute zero, the entropy of a system approaches a constant minimum.
4) The zeroth law: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

3. How is thermodynamics used in everyday life?

Thermodynamics is used in a variety of everyday applications, including refrigerators, air conditioners, car engines, and power plants. It also plays a role in cooking, as the transfer of heat is essential for cooking food properly.

4. What is the difference between heat and temperature?

Heat is a form of energy that is transferred from one object to another due to a difference in temperature. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in a substance. In other words, heat is the energy being transferred, while temperature is a measure of how hot or cold something is.

5. How does thermodynamics relate to other branches of science?

Thermodynamics is closely related to other branches of science, including chemistry, biology, and engineering. It is used to understand and explain the behavior of matter and energy in these fields, and its laws are fundamental principles in many scientific theories and models.

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