Understanding Constant Temperature in Ideal Gas Filling Process

[thinkingcap81]

I'm trying to solve a problem where a perfect ideal gas is entering an initially evacuated rigid vessel. The input pressure and temperature are P_i and T_i which are constant. The incoming mass M_i is an arbitrary function of time.

When i solve this, i get the temperature inside the container as (C_p/C_v)T_i which is same from the beginning till the end of the filling process.

I am unable to physically understand how the temperature in the container is supposed to be constant. Isn't the ideal gas entering the rigid vessel undergoing free expansion at the first instant and then it gradually becomes more difficult to pump the gas in? So how can the temperature inside the container be constant?

I know that some books talk of imagining a piston pushing the gas in hand hence it is doing flow work, but i cannot visualize the process especially in the context of the present problem.

 

[Chestermiller]

I'm trying to solve a problem where a perfect ideal gas is entering an initially evacuated rigid vessel. The input pressure and temperature are P_i and T_i which are constant. The incoming mass M_i is an arbitrary function of time.

When i solve this, i get the temperature inside the container as (C_p/C_v)T_i which is same from the beginning till the end of the filling process.

I am unable to physically understand how the temperature in the container is supposed to be constant. Isn't the ideal gas entering the rigid vessel undergoing free expansion at the first instant and then it gradually becomes more difficult to pump the gas in? So how can the temperature inside the container be constant?

I know that some books talk of imagining a piston pushing the gas in hand hence it is doing flow work, but i cannot visualize the process especially in the context of the present problem.

It really seems to me that you have doubts about this because it goes against your intuition, but nothing concrete. Are you saying that you are uncomfortable with the open system version of the first law of thermodynamics?

With regard to the gas entering the valve being pushed from behind, imagine that there is an imaginary membrane separating the gas entering the valve from the gas behind it. The gas behind it acts like a piston to push it into the valve.