# Solve Asymmetric Piston Problem for SL

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• SchroedingersLion
In summary, the conversation discusses a textbook problem involving a diathermal piston and the ideal gas law. The problem asks for the final temperature and pressures of the gas in both chambers, as well as the piston displacement. The conversation also mentions applying the ideal gas law to find a second equation and using the entropy function to potentially solve the problem. The author is unsure of what the expected solution is.
SchroedingersLion
Greetings!

Can you help me understand what this text book problem asks of me?

The situation was considered in the text: In equilibrium, the forces on both sides of the piston are equal: ##A_1P_1 = A_2P_2##.
This is the first equation. It should also answer part 3 of the question. The piston allows heat exchange, so that in equilibrium I have ##T_1=T_2##. This should answer part 2. To get a second equation to answer part one, I can just apply the ideal gas law to the first equation to get
$$A_j\frac{N_j}{V_j} = A_k\frac{N_k}{V_k}.$$

I feel like this is way too easy and I am missing something... I don't know what the author wants me to do. I should note that he derived the entropy function S(E,V,N) of the ideal gas, and also the three partial derivatives such as ##\left(\frac{\partial S}{\partial V}\right)_{E,N}=\frac {P} {T} ##, so maybe he expects some more wizardry with them?SL

Delta2
The problem says the piston is diathermal so ##T_1 \neq T_2##.

EDIT I confused it with adiabatic.

Last edited:
Delta2
anuttarasammyak said:
The problem says the piston is diathermal so ##T_1 \neq T_2##.
Diathermal means that the temperature ARE equal in the end.

Delta2 and anuttarasammyak
I don't know what the author had in mind, but here are some thoughts on how I would approach this problem (assuming the same gas species is in both chambers). For the final temperature, I would have $$T=\frac{(E_1+E_2)}{C_v(N_1+N_2)}$$
For the final volumes, I would have: $$V_1=V_{10}+A_1\delta$$$$V_2=V_{20}-A_2\delta$$where ##\delta## is the displacement of the piston. So, for the final pressures, we would have: $$P_1=\frac{N_1RT}{V_1}$$$$P_2=\frac{N_2RT}{V_2}$$subject to $$P_1A_1=P_2A_2$$This provides sufficient information to determine the piston displacement ##\delta##.

Delta2 and SchroedingersLion
Thanks Chestermiller!

The author did not ask for the displacement, so it is really unclear what he even expects. Glad to know that I did not miss something obvious.

To get the final pressure, you need to first solve for the displacement.

## 1. What is an asymmetric piston problem?

An asymmetric piston problem is a type of mechanical engineering problem that involves finding a solution for a piston that is not symmetrical in shape or weight distribution. This can affect the performance and efficiency of the piston and requires careful analysis and calculation to solve.

## 2. Why is it important to solve asymmetric piston problems?

Solving asymmetric piston problems is important because it can greatly impact the functionality and efficiency of a piston. If left unresolved, it can lead to uneven wear and tear, decreased performance, and potential safety hazards.

## 3. What are the common methods for solving asymmetric piston problems?

There are several methods for solving asymmetric piston problems, including mathematical modeling, computer simulations, and physical testing. Each method has its own advantages and limitations, and the most suitable approach will depend on the specific problem and resources available.

## 4. What are some key factors to consider when solving asymmetric piston problems?

When solving asymmetric piston problems, it is important to consider factors such as material properties, weight distribution, friction, and pressure differentials. These factors can greatly impact the performance of the piston and must be carefully analyzed and accounted for in the solution.

## 5. Are there any tips for successfully solving asymmetric piston problems?

Some tips for successfully solving asymmetric piston problems include thoroughly understanding the problem, using accurate and precise measurements, and considering multiple solutions before deciding on the best one. It is also important to regularly test and monitor the piston's performance after implementing a solution to ensure it is functioning properly.

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