- #1

GravityX

- 19

- 1

- Homework Statement:
- Calculate the limit of ##P## when ##a_0 \rightarrow 0## and ##M,n \rightarrow \infty## with ##a=a_0n## and ##L=a_0*M##.

- Relevant Equations:
- none

Hi,

I had to calculate the entropy in a task of a lattice gas and derive a formula for the pressure from it and got the following

$$P=\frac{k_b T}{a_0}\Bigl[ \ln(\frac{L}{a_0}-N(n-1)-\ln(\frac{L}{a_0}-nN) \Bigr]$$

But now I am supposed to calculate the following limit

$$\lim\limits_{a_0 \rightarrow \infty}{} \lim\limits_{M \rightarrow \infty}{} \lim\limits_{n \rightarrow \infty}{\frac{k_b T}{a_0}\Bigl[ \ln(\frac{L}{a_0}-N(n-1)-\ln(\frac{L}{a_0}-nN) \Bigr]}$$

So not the limit for ##a_0## , ##M## and ##n## but all at the same time.

Should I first calculate the limit for one, say for ##a_0## and what I got for that, the limit for ##M## or better said ##L## etc?

I had to calculate the entropy in a task of a lattice gas and derive a formula for the pressure from it and got the following

$$P=\frac{k_b T}{a_0}\Bigl[ \ln(\frac{L}{a_0}-N(n-1)-\ln(\frac{L}{a_0}-nN) \Bigr]$$

But now I am supposed to calculate the following limit

$$\lim\limits_{a_0 \rightarrow \infty}{} \lim\limits_{M \rightarrow \infty}{} \lim\limits_{n \rightarrow \infty}{\frac{k_b T}{a_0}\Bigl[ \ln(\frac{L}{a_0}-N(n-1)-\ln(\frac{L}{a_0}-nN) \Bigr]}$$

So not the limit for ##a_0## , ##M## and ##n## but all at the same time.

Should I first calculate the limit for one, say for ##a_0## and what I got for that, the limit for ##M## or better said ##L## etc?