/sci/ - Science & Math

>>11353618
Intersection

>>11334290
Oh right...
>So what is a linear circuit then?
A circuit that can be modeled by a linear ODE. Linear ODEs are called such because any linear combination of homogeneous solutions is also a solution. Which is exactly what linearity is all about.

>>11228960
It isnt exactly intuitive though, is it? yw :*

>>11201098
>but I want to know if I need to recalculate the partial density after I get the answer.
If you are iterating, yes.
>isn't partial density [math] \rho_{g}.X_{i} [/math]
Assuming ideal gas conditions, we use Amagat's law for partial volume.
[eqn] \frac{V_i}{V}=\frac{n_i RT/P}{n RT/P}=\frac{n_i}{n}=y_i [/eqn]
where y_i is the molar fraction and [math]V=\sum V_i[/math] . But, [math] V_i=\nu_im_i=m_i/\rho_i [/math] where nu is specific volume and rho density. So
[eqn] \frac{V}{V_i}=\frac{m/\rho}{m_i/\rho_i}=\frac{\rho_i m}{\rho m_i} [/eqn]
therefore
[eqn] \rho_i=\rho\cdot\frac{V}{V_i}\cdot\frac{m_i}{m}=\rho\cdot\frac{w_i}{y_i}=\rho\cdot\frac{M_i}{M}=\rho\cdot X_i [/eqn]
So, if Xi is the ratio of the molar mass of the species to the average molar mass of the total, then the answer to your second question is "yes." Sorry, I was phone posting the other day at very hihg speed and thought you meant mass molar fraction by the big X. Xi is NOT molar fraction.

>>11206841
>runge kutta
plot the value of the functions for each time step. for small time steps, you get a smooth looking curve.

Grounded and resistor color-code pilled