Change in number of microstates

[Kara386]

Homework Statement

An isolated macroscopic system at 300K absorbs a photon with $\lambda = 550nm$. What is the relative increase $\frac{\Delta \Omega}{\Omega}$ in microstates.

Homework Equations

The Attempt at a Solution

The energy of the photon is $E = \frac{hc}{\lambda}$ so that would be the change in internal energy. And $dU = TdS - pdV$ but I assume $dV = 0$ so $dU = TdS$.

$S = k \ln(\Omega)$ so I think $dS = k d\ln(\Omega)$:

$d \ln(\Omega) = \frac{hc}{\lambda T}$
If that's all ok, I don't know how to get from there to $\Delta \Omega$ or how to get the relative increase in $\Omega$! Thanks for any help!

 

[TSny]

$d \ln(\Omega) = \frac{hc}{\lambda T}$
...I don't know how to get from there to $\Delta \Omega$ or how to get the relative increase in $\Omega$! Thanks for any help!

You just need to carry out the differential of $\ln \Omega$. You don't need to find $\Delta \Omega$, you only need $\frac{\Delta \Omega}{\Omega}$.
https://en.wikipedia.org/wiki/Differential_of_a_function

 

[Kara386]

You just need to carry out the differential of $\ln \Omega$. You don't need to find $\Delta \Omega$, you only need $\frac{\Delta \Omega}{\Omega}$.
https://en.wikipedia.org/wiki/Differential_of_a_function

Thank you for that link! Been trying to find out what it's called when you put a 'd' in front of variables for ages. And how to then actually do something with it. Thanks for your help!