Solving Part B of PV=NkbT: An Explanation

[Junkwisch]

Homework Statement

"see attachment"

Homework Equations

PV=NkbT
Change in entropy = Boltzmann Constant x In(Macrostate)

The Attempt at a Solution

for part A, I knew that PV=NKbT

giving that pressure is 101300Pa volume is 1*10^-3 m^3, Kb is 1.38*10^-23 and T=300K
I find N to be 2.446*10^22 atoms


the problem I have is with part B

the question states that microstate is proportion to V^N where N is the number of atom I found in part A, and V is the volume which is 1*10-9 m^3. Thus V^N is a very small number which is pretty much zero. Change in entropy = Boltzmann Constant x In(Macrostate), since Macrostate is zero, there is an error in this calculation. Since In(0) is undefined. What am I suppose to do in this question??

 

[Junkwisch]

I forgot to attach the question, here it is

 

[Oxvillian]

Hi Junkwisch!

Always in physics things are only big or small relative to other things. The numerical value of $V^N$ depends entirely on what units you're using.

Perhaps you can simplify $\ln\left(V^N\right)$ without making an approximation?

 

[vela]

Change in entropy = Boltzmann Constant x In(Macrostate)

You should check that you have the correct relationship here. How can the left side of the equation be a change when there's no corresponding change present on the righthand side of the equation? Also, what is "Macrostate" supposed to represent?

 

[paranormal]

As a scientist, it is important to recognize when a calculation may lead to an undefined or nonsensical result. In this case, the calculation for change in entropy is not applicable because the macrostate is zero, which is not a physically meaningful value. This could be due to the extremely small volume used in the calculation, which makes the macrostate approach zero.

To address this issue, I would suggest using a larger volume for the calculation, or considering a different approach altogether. Additionally, it is important to remember that these equations and calculations are simplifications of complex systems, and may not always accurately represent real-world situations. It is important to critically evaluate the results and consider any potential limitations or errors in the calculations.