My Math Forum  

Go Back   My Math Forum > Science Forums > Chemistry

Chemistry Chemistry Forum


Thanks Tree1Thanks
  • 1 Post By DarnItJimImAnEngineer
Reply
 
LinkBack Thread Tools Display Modes
November 6th, 2019, 12:12 PM   #1
Newbie
 
Joined: Nov 2019
From: UK

Posts: 1
Thanks: 0

Thermal Conductivity

Hello All

Currently trying to get through the question below, but any formula I find is too complex for the brief detail given, with regard thermal conductivity of gases.


It is proposed to use a katharometer to measure the amount (about 5%) of oxygen in nitrogen, in the presence of a small amount (0.5%) hydrogen. How constant would the proportion of hydrogen have to be in order to limit errors in measurement of % oxygen to + 0.1%?

The thermal conductivities are:

nitrogen 0.993
oxygen 1.052
hydrogen 6.993
Baggy is offline  
 
November 6th, 2019, 06:15 PM   #2
Senior Member
 
Joined: Jun 2019
From: USA

Posts: 386
Thanks: 211

Question 1. Are you using a specific model for the thermal conductivity of a mixture of gases? If we were looking for specific heats, energy, or similar properties of a mixture of ideal gases, we would use a mass-weighted average. In this type of model, the thermal conductivity would look something like this:
$\displaystyle k_{mixture} = [1-f_{O2}-f_{H2}] k_{N2} + f_{O2} k_{O2} + f_{H2} k_{H2}$, where $f_i$ (or $mf_i$, or $c_i$) is the mass fraction of gas $i$.

However, I also know of literature that claims that kinetic theory does not predict the thermal conductivity of gas mixtures well, and slightly more complex empirical formulas have been proposed.

Either way, you are going to have some equation $k_{mixture} = k(f_{N_2},f_{O_2},f_{H_2})$.

Since no information was given about the accuracy of the katharometer or the Wheatstone bridge, I assume the question is about keeping the conductivity of the mixture sufficiently constant.
If $f_{H2} = 0.005 \pm u_{fH2}$, then barring any other sources of uncertainty,
$\displaystyle k_{mixture} = k(0.945,0.05,0.005) \pm \frac{\partial k_{mixture}}{\partial f_{H2}} u_{fH2}$.
Whatever equation you use for the thermal conductivity of the mixture, take the partial derivative with respect to the hydrogen mass fraction and evaluate at the nominal conditions. Then,
$\displaystyle u_k = \frac{\partial k_{mixture}}{\partial f_{H2}} u_{fH2}$.

But then, you are going to measure (indirectly) the thermal conductivity, and back out the mass fraction of the oxygen, and it is this number you want to keep within ±0.1 %.
$\displaystyle u_{fO2} = \frac{\partial f_{O2}}{\partial k_{mixture}} u_k$.

So, evaluate both partial derivatives at the nominal conditions, and solve,
$\displaystyle \left| \pm 0.001 \right| \geq \left| \frac{\partial f_{O2}}{\partial k_{mixture}} \frac{\partial k_{mixture}}{\partial f_{H2}} u_{fH2} \right|$
for the maximum allowable uncertainty $u_{fH2}$.


If your question was specifically about how to calculate the thermal conductivity of the mixture, then I can guide you to some literature, but I am not an expert and could not guarantee the reliability of one model over another.
Thanks from Baggy
DarnItJimImAnEngineer is offline  
Reply

  My Math Forum > Science Forums > Chemistry

Tags
conductivity, thermal



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Thermal Expansion Grntxavier Physics 1 October 16th, 2017 03:48 AM
Another thermal expansion question hyperbola Physics 4 September 16th, 2015 03:02 AM
Thermal expansion question hyperbola Physics 0 September 12th, 2015 09:47 AM
Thermal Equilibrium rnck Physics 3 June 15th, 2011 07:55 AM
Define thermal conductivity . Also on what factor 'K' depend r-soy Physics 0 March 17th, 2011 06:22 AM





Copyright © 2019 My Math Forum. All rights reserved.