Derive Entropy Change for Ideal Monatomic Gas

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SUMMARY

The discussion focuses on deriving the change in entropy for a monatomic ideal gas transitioning from state 1 (pressure p1, volume V1) to state 2 (pressure p2, volume V2). The correct expression for the change in entropy is ΔS = Cv ln(T2/T1) + nR ln(V2/V1). A participant initially miscalculated the equation by omitting the unit of moles in the volume ratio, leading to confusion. Ultimately, the issue was resolved by recognizing the need to incorporate the correct assumptions regarding moles in the derivation process.

PREREQUISITES
  • Understanding of thermodynamic concepts, specifically entropy and ideal gases.
  • Familiarity with the first law of thermodynamics and its application to ideal gases.
  • Knowledge of the specific heat capacities, Cv and R, and their units.
  • Ability to manipulate logarithmic equations in thermodynamic contexts.
NEXT STEPS
  • Study the derivation of the ideal gas law and its implications for entropy changes.
  • Learn about the specific heat capacities of gases, focusing on Cv for monatomic gases.
  • Explore the application of the Clausius definition of entropy in thermodynamic processes.
  • Investigate the implications of assumptions in thermodynamic calculations, such as the mole assumption.
USEFUL FOR

Students and professionals in thermodynamics, physicists, and engineers who are studying or working with ideal gases and entropy calculations.

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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 = Cv ln(T2/T1) + nRln(V2/V1)

In my attempt, I am retrieving ΔS = Cv 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?
 
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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.
 
What are the units of Cv, R, and ΔS?

What is the exact statement of the problem?

Chet
 
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".
 

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