Temperature and Mass Flow effect on Pressure

[samshree]

Hello,

I am trying to create a theoretical model of pressurizing air in a constant volume tank to a pre-set pressure. We are increasing the pressure using a standard pressure regulator. From the equation PV=nRT I know that an increase in pressure at a constant volume can result from an increase in mass and/or temperature. In our model I believe the main source of pressure increase is due to mass increase, but I have experienced and increase of temperature due to recompression as well. Is there a way to determine how much of the pressure increase is due to mass flow and how much is due to temperature increase? And is there an equation or model I could use to predict how much the temperature of the gas will increase when the pressure increases a certain amount?

 

[boneh3ad]

There are models for this, particularly if you can ensure the tank is adiabatic (no heat transfer in or out of the tank). In that case you can treat the problem as isentropic and use the ideal gas law and the isentropic relations to get what you are after. For example, you know one form of the ideal gas law is $p = \rho R T$ where $R$ is the specific gas constant. For an isentropic process in an ideal gas, you have the following relationships:
$$\dfrac{p_2}{p_1} = \left(\dfrac{\rho_2}{\rho_1}\right)^{\gamma} = \left(\dfrac{T_2}{T_1}\right)^{\gamma/(\gamma-1)}$$
where $\gamma = c_p/c_v$. That should get you where you need to go.

 

[samshree]

Will this still apply to an open system where mass is flowing into the control volume? The temperature and density are changing simultaneously. I have seen these equations before but I thought they were for a closed system

 

[boneh3ad]

No it still works.

 

[alphy]

Hello,

Thank you for sharing your theoretical model with me. It is interesting to see how you are incorporating the ideal gas law (PV=nRT) into your model for pressurizing air in a constant volume tank. To answer your questions, the effect of temperature and mass flow on pressure can be determined by using the ideal gas law and the continuity equation.

The ideal gas law, as you mentioned, states that an increase in pressure can result from an increase in temperature or mass. This is because an increase in temperature causes the gas molecules to move faster and collide more frequently with the walls of the container, resulting in an increase in pressure. Similarly, an increase in mass means there are more gas molecules in the container, leading to more collisions and an increase in pressure.

To determine the specific contributions of temperature and mass flow to the pressure increase in your model, you can use the continuity equation, which states that the mass flow rate into a system must equal the mass flow rate out of the system. By measuring the mass flow rate into the tank and the mass flow rate out of the tank, you can determine the mass flow rate that is contributing to the pressure increase.

As for predicting the temperature increase when the pressure increases a certain amount, this can be done by rearranging the ideal gas law to solve for temperature (T = PV/nR). By plugging in the initial pressure, volume, and number of moles, and using the new pressure as P, you can calculate the corresponding temperature increase.

I hope this helps in your theoretical model and further research. Best of luck!