Final State Tank Homework: Solving E_out,mass Integral

[Art_]

Homework Statement

Given a tank filled with gas, you are to pump out a given amount and find the final state of the tank. Given the volume, gas (non-ideal), amount of gas in tank, flow rate, temperature and pressure, all at state 1. We can find density at state 2 from the tables, but we need another quantity. So we can also solve for enthalpy.

Homework Equations

E_out,mass = [itex]\int h + V/2 + gz dm[/itex]
The KE and PE can be neglected due to high flow rate, so the equation simplifies to
E_out,mass = [itex]\int h dm[/itex]
but since h is not constant I am confused how to integrate this, and find h.

The Attempt at a Solution

I am trying to integrate numericaly but am not sure how to approch finding the intermidiate values of h.

Thank you for the help.

 

[Simon Bridge]

Well what does h depend on?

 

[Art_]

Well h=u+pv, with u being the internal energy and p pressure and volume is constant for the tank.

 

[Simon Bridge]

Well you need to express the things that change with m in terms of m... or, express dm in terms of the things that change.

 

[rezeew]

It seems like you are on the right track by trying to integrate numerically. To find the intermediate values of h, you can use the ideal gas law and the given properties (volume, gas amount, temperature, and pressure) to calculate the density at each step. Then, using the density and the given flow rate, you can calculate the mass flow rate at each step. Finally, you can use the mass flow rate and the given enthalpy to calculate the specific enthalpy at each step, which you can then use in your integral. This approach should give you a numerical solution for the final state of the tank.

 

[DeeNos]

I would suggest approaching this problem by first understanding the physical principles involved. In this case, we are dealing with a non-ideal gas, which means that its behavior cannot be accurately described by the ideal gas law. Therefore, we need to use more advanced equations, such as the Van der Waals equation, to calculate the properties of the gas.

Once we have a better understanding of the behavior of the gas, we can then use the given information (volume, amount of gas, flow rate, temperature, and pressure) to determine the initial state of the gas in the tank. From there, we can use the equations of thermodynamics to calculate the final state of the gas after pumping out a given amount.

In terms of the integral for E_out,mass, it is important to note that enthalpy (h) is not a constant and will change as the gas is pumped out of the tank. Therefore, we cannot simply integrate h to find E_out,mass. Instead, we need to break down the integral into smaller steps, where we can use the Van der Waals equation and other relevant equations to calculate the change in enthalpy at each step. This will allow us to numerically integrate and find the final value of E_out,mass.

In summary, as a scientist, I would suggest approaching this problem by first understanding the physical principles involved, using relevant equations to calculate the properties of the gas, and breaking down the integral into smaller steps to accurately calculate the final state of the tank.