Adiabatic process btwn 2 containers

In summary, the conversation discusses finding the final equilibrium pressure after opening a valve between two cylinders of equal volume. The correct method is PiV1^gamma = PfV1^gamma+PfV2^gamma, which may seem to contradict the formula PV^gamma = constant for an adiabatic process. However, this is due to the change in the number of moles of gas in the first cylinder, while total internal energy remains constant. The scenario is an example of "adiabatic free expansion" where no work is done since there is no piston involved. The person expressing gratitude for the help received in understanding the concept.
  • #1
Kenny Lee
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Two cylinders of equal volume are connected by a valve. We are given the pressure for one of them, and then told to find the final equilibrium pressure after the valve is opened. Adiabatic process may be assumed.

I know the solution, but not sure why its that way... initially, I tried PiV1^gamma = Pf(V1+V2)^gamma. But the correct method is: PiV1^gamma =PfV1^gamma+PfV2^gamma.

Someone please tell me how the latter is valid. It seems to me that it violates the basic formula PV^gamma = constant.
 
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  • #2
PV^gamma is constant for an adiabatic process if n is constant. Opening up the chambers changes the number of moles of gas in the first cylinder. That which stays constant for the two chambers together is total internal energy.

Edit: hmm, I'm assuming that this was an example of "adiabatic free expansion." Was there total vacuum in the second cylinder? IF so, then in this situation, no work is done when the gas expands (you see, there is no piston involved). That's why internal energy remains constant.
 
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  • #3
thanks, I get it now. Hey, youve helped me out quite a few times already. Just so you know, I genuinely appreciate it
 

FAQ: Adiabatic process btwn 2 containers

What is an adiabatic process between two containers?

An adiabatic process between two containers is a thermodynamic process in which there is no transfer of heat or energy between the two containers. This means that the temperature, pressure, and volume of the gas inside each container will change without any external heat source or work being applied.

What is the difference between adiabatic and isothermal processes?

The main difference between adiabatic and isothermal processes is that in an adiabatic process, there is no transfer of heat between the system and its surroundings, while in an isothermal process, the temperature remains constant.

What is the equation for an adiabatic process?

The equation for an adiabatic process is given by P1V1^γ = P2V2^γ, where P1 and V1 are the initial pressure and volume of the gas, P2 and V2 are the final pressure and volume, and γ is the adiabatic index or ratio of specific heats of the gas.

What is the ideal gas law and how does it relate to adiabatic processes?

The ideal gas law is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. This law relates to adiabatic processes because it can be used to calculate the pressure, volume, and temperature of an ideal gas at different points in an adiabatic process.

What factors can affect the outcome of an adiabatic process between two containers?

The outcome of an adiabatic process between two containers can be affected by the initial pressure and volume of the gas, the adiabatic index, and any work or external forces applied to the system. Additionally, the type of gas and its specific heat capacity can also impact the outcome of the process.

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