Derive Entropy Change for Ideal Monatomic Gas

[SalfordPhysics]

A Monatomic gas passes from state 1 (pressure p₁, volume V₁) to state 2 (p₂, V₂).
Derive an expression for the change in entropy of a monatomic ideal gas.

The required final equation is: ΔS = C_v ln(T₂/T₁) + nRln(V₂/V₁₎

In my attempt, I am retrieving ΔS = C_v ln(T₂/T₁) + Rln(V₂/V₁₎
i.e.; the unit of moles not present in the "(V₂/V₁₎" term.
Is the given form to obtain incorrect or am I making a very silly mistake to do with the prior assumptions?

 

[Orodruin]

It is very difficult to help you if you do not state how you are arriving at your expression.

For the future, also leave the headings of the homework template in your post.

 

[Chestermiller]

What are the units of C_v, R, and ΔS?

What is the exact statement of the problem?

Chet

 

[SalfordPhysics]

Its not a problem now I figured things out, the problem was my solved form wasn't exactly as required, but like I thought I was making a mistake with a moles = 1 assumption in another derivation that i was using a a "subroutine".

 

[paranormal]

Your derivation is correct. The "(V2/V1)" term should not have a unit of moles because it is a ratio of volumes, not a ratio of moles. The correct form of the equation is ΔS = Cv ln(T2/T1) + nRln(V2/V1), where n is the number of moles of gas. This equation takes into account both the change in temperature and the change in volume of the gas, and it is a valid expression for the change in entropy of an ideal monatomic gas.