Heat Transfer in Ideal Gases: An Example of Path Dependence

In summary: The heat path dependency of a process is when the final state of the process is different than the initial state. This can be done by changing either the temperature or pressure, but it must be done in a specific order. In the first case, you change the temperature and then change the pressure. In the second case, you change the pressure and then change the temperature. In both cases, you reach the final state.
  • #1
hiba fatima
3
1
< Mentor Note -- Posts split off from an old thread to preserve very good helpful responses...>

how is heat path dependent?prove with an example?
 
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  • #2
gerardpc said:
I've read a solution of a problem, in which there are two different gases in a container, initally at equilibrium and separated by an adiabatic fix wall. At some time, this wall is changed by a diathermic mobile wall, so the equilibrium point changes. You have to find the final state of the gases, given the initial volumes, temperatures and pressions.

Then the solution says: we will divide the process in two parts: first an isochoric process and after that and isothermal one. But it is clear that pressure and temperature evolve at the same time.
I'm making a bit of a mess here: is it path dependent or indpendent? In a generic process, when is it path independent and when it is not? And why?
Consider an ideal gas at initial state (p1,V1,T1). We want to change the state to (p2,V2,T2).

We can do this in many ways, but let's pick two in particular :
1. we can change the temperature at constant V1 (isochoric) until p = p2, then, holding p constant, change the temperature some more until V = V2. We have reached (p2,V2,T2).
2. we can change the temperature at constant p1 (isobaric) until V = V2, then, holding V constant, change temperature some more until p = p2. We have again reached (p2,V2,T2).
In both cases we went from state (p1,V1,T1) to (p2,V2,T2).
Can you compute the heat and work required in both processes?
 
  • #3
thanx ... but you did not clear the point that the heat is path dependent...means we go to the same state in both cases...but what is the difference in both cases that makes the heat path dependent...
 
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  • #4
hiba fatima said:
thanx ... bt u did not clear the point that the heat is path dependent...means we go to the same state in both cases...but what is the difference in both cases that makes the heat path dependent...
The difference is in one case we change p first and then V, in the other we change V first and then p. The sequence makes it different. Compute W and Q for both cases and you will see.
 
  • #5
i could not do it :(
 
  • #6
hiba fatima said:
i could not do it :(
What is the area under a p-V curve going from a state 1 to a state 2?
 
  • #7
I assume you are dealing with ideal gases. If the gases are in a rigid container, how much external work do the combination of gases do on the surroundings? Assuming that the container is adiabatic, how much heat passes through the walls of the container. From the first law of thermodynamics, what is the change in internal energy for the combination of gases when the system finally equilibrates? If the wall is mobile and diathermal, how do the temperatures and pressures in the two compartments compare at the final equilibrium state?

Chet
 

1. What is the definition of thermodynamics?

Thermodynamics is a branch of physics that deals with the study of heat, work, and energy in a system. It also describes how these quantities are related to each other and how they affect the behavior of matter.

2. What are the laws of thermodynamics?

The first law states that energy cannot be created or destroyed, only transferred from one form to another. The second law states that the total entropy of a closed system will always increase over time. The third law states that the entropy of a perfect crystal at absolute zero temperature is zero.

3. What is the difference between heat and temperature in thermodynamics?

Heat is the transfer of energy between two objects due to a temperature difference. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in a system. In other words, heat is a form of energy, while temperature is a measure of how much heat is present in a system.

4. How does thermodynamics apply to everyday life?

Thermodynamics applies to everyday life in many ways, such as in cooking, heating and cooling systems, and even the human body. It helps us understand how energy is transferred and transformed, and how it affects the behavior of matter in our daily lives.

5. What are some practical applications of thermodynamics?

Some practical applications of thermodynamics include power generation, refrigeration and air conditioning, and chemical reactions. It also plays a crucial role in the design and efficiency of engines, turbines, and other industrial processes.

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