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.