# Finding Final Temp. Distribution After Thermal Equilibrium

• niazaliahmed
In summary, the conversation discusses finding the final temperature distribution after thermal equilibrium in an isolated system. The correct unit of energy is Joules, and the correct unit of temperature is Kelvin. The system will reach a state of maximum entropy and uniform temperature, and the initial energy in the system must remain constant.
niazaliahmed

The above diagram shows the problem description.

I have to find the final temperature distribution after thermal equilibrium.

I am assuming that the thermal energy is conserved but not the temperature.(Correct me if I am wrong)

Energy of the materials at initial state is (Refer Image)

For material 1 - m.Cp.T = 100*1*45 W = 4500W
For material 2 - m.Cp.T = 200*1*50 W = 10000W

So the system would achieve equilibrium when the energy in both material are same i.e. 7250W

If that happens Material 1 would be at a temperature of 72.5 C
Material 2 would be at a temperature of 36.25 C

I know that this method is wrong indeed. But can anyone explain me why we would conserve the temperature instead of energy of the system??

For starters the correct unit of energy is Joules(J) not Watts(W). The correct unit of temperature is Kelvin(K) not Celsius(C). If I remember correctly you add 273 to a temperature in C to get it into K.

Since the system (meaning both blocks) is isolated, the the total internal energy must remain constant. An isolated system will eventually reach a state of maximum entropy (and therefore uniform temperature).

So the initial energy in the system is:

m1c1T1 + m1c1T2 = a constant

and after reaching equilibrium

(m1c1+m2c2)T = the same constant

thus equate the two and solve for T.

## 1. What is thermal equilibrium?

Thermal equilibrium is a state in which two or more objects or systems are in contact and have reached the same temperature. This means that there is no net flow of heat between the objects or systems.

## 2. How do you calculate the final temperature distribution after thermal equilibrium?

To calculate the final temperature distribution, you would need to use the laws of thermodynamics and the specific heat capacities of the objects or systems in question. This involves calculating the heat gained or lost by each object and setting it equal to the heat gained or lost by the other objects, until all temperatures are equal.

## 3. What factors affect the final temperature distribution?

The final temperature distribution is affected by the initial temperatures of the objects or systems, their specific heat capacities, and the rate at which heat is transferred between them. Other factors such as insulation and external heat sources can also impact the final temperature distribution.

## 4. Is it possible for objects to reach different final temperatures in thermal equilibrium?

Yes, it is possible for objects or systems to reach different final temperatures in thermal equilibrium. This is because the rate of heat transfer and the specific heat capacities of the objects can vary, leading to different amounts of heat gained or lost and thus resulting in different final temperatures.

## 5. Why is it important to understand thermal equilibrium and final temperature distribution?

Understanding thermal equilibrium and final temperature distribution is important in various scientific fields, such as thermodynamics and engineering. It allows us to predict and control the behavior of heat transfer in systems, which is crucial in many practical applications, such as designing efficient heating and cooling systems.

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