Thermodynamics Finding a fundamental equation.

AI Thread Summary
The discussion centers on finding a fundamental equation in thermodynamics that incorporates temperature (T), pressure (p), and chemical potential (μ) instead of the number of molecules (N). The Gibbs free energy (G) is identified as a key function for the natural variables (T, p, N), but the focus shifts to controlling concentrations through μ. Participants suggest using a Legendre transform to transition from N to μ, similar to how G is used instead of enthalpy (H) when T is the desired variable. The conversation emphasizes the importance of understanding Legendre transforms to tackle this problem effectively. Overall, the thread provides insights into adapting thermodynamic equations for biological systems.
corr0105
Messages
7
Reaction score
0
Thermodynamics! Finding a fundamental equation.

This is the question:
"While he Gibbs free energy G is the fundamental function of the atral variables (T,p,N), (T=temperature, p=pressure, N=number of molecules), growing biological cells often regulte not the numbers of molecules N, but the chemical potentials μ. That is, they control concentrations. What is the fundamental function Z of natural variables (T,p,μ)?

I know a few equations that deal with Gibbs free energy:
G=H-TS
G=\sumμN

Basically, I have no idea where to start with this problem. If anyone can give me a push in the right direction that would be much appreciated!
 
Physics news on Phys.org
You need to apply a Legendre transform (so check out what this is). An example of of Legendre transform: we use G instead of H because we wish to use T as a natural variable instead of S. Now you've learned that you'd also like to use μ instead of N. This should be enough to get you started.
 
Thanks so much, I looked up how to use Legendre transforms for this type of problem and eventually figured it out (not to mention learned something!). Thanks for your help!
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top