# Flow work in Thermodynamics

• thinkingcap81
In summary: This way, the gas entering the valve is doing flow work and the gas behind it is doing positive pressure work.

#### 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 Pi and Ti which are constant. The incoming mass Mi is an arbitrary function of time.

When i solve this, i get the temperature inside the container as (Cp/Cv)Ti 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.

thinkingcap81 said:
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 Pi and Ti which are constant. The incoming mass Mi is an arbitrary function of time.

When i solve this, i get the temperature inside the container as (Cp/Cv)Ti 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.

## What is flow work in thermodynamics?

Flow work, also known as "pressure-volume" work, is the work done by a fluid as it flows through a boundary. It is a type of mechanical work that is associated with the movement of a fluid across a boundary.

## How is flow work related to thermodynamics?

In thermodynamics, flow work is an important concept as it is a form of energy that can be transferred between a system and its surroundings. It is also a key component in the calculation of energy balances and can impact the efficiency of a system.

## What is the equation for calculating flow work?

The equation for calculating flow work is W = PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume. This equation applies to both compressible and incompressible fluids.

## What is the difference between flow work and boundary work?

Flow work and boundary work are both forms of mechanical work, but they differ in their definitions and applications. While flow work is associated with the movement of a fluid through a boundary, boundary work is associated with changes in the volume or pressure of a system due to external forces.

## How is flow work calculated in real-world applications?

In real-world applications, flow work is typically calculated by measuring the pressure and volume of a fluid at different points in a system, and then using the equation W = PΔV to determine the work done by the fluid.