Final State Tank Homework: Solving E_out,mass Integral

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of the final state of a gas-filled tank after pumping out a certain amount of gas. Participants explore the integration of enthalpy in the context of non-ideal gas behavior, considering various state variables such as temperature, pressure, and volume.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant states the need to find the final state of the tank by integrating the expression for energy out, specifically focusing on enthalpy.
  • Another participant questions what enthalpy (h) depends on, prompting further exploration of the relationship between state variables.
  • A different participant provides a definition of enthalpy as h = u + pv, noting that internal energy (u) and pressure (p) are relevant, while volume is constant for the tank.
  • One participant suggests that it is necessary to express the changing variables in terms of mass (m) or to express dm in terms of those changing variables to facilitate integration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to approach the integration of enthalpy, and multiple viewpoints on the dependencies of enthalpy and the integration process are presented.

Contextual Notes

There are limitations regarding the assumptions made about the gas behavior, the dependency of enthalpy on various state variables, and the need for further clarification on how to express changing quantities in terms of mass.

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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 = \int h + V/2 + gz dm
The KE and PE can be neglected due to high flow rate, so the equation simplifies to
E_out,mass = \int h dm
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.
 
Last edited:
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Well what does h depend on?
 
Well h=u+pv, with u being the internal energy and p pressure and volume is constant for the tank.
 
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.
 

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