Change in Entropy of an expanding gas

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SUMMARY

The change in entropy for four moles of an ideal gas expanding at constant temperature until its pressure is halved can be calculated using the formula ΔS = nrT ln(Vf/Vi). Given that the pressure ratio is known, the corresponding volume ratio can be derived from the ideal gas law, PV = constant. The assumption of a reversible expansion is crucial for applying the entropy change formula correctly. The user inquired about alternative methods involving pressure change, but the established approach using volume ratios is definitive.

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  • Understanding of ideal gas laws (PV = nRT)
  • Knowledge of thermodynamic principles, specifically entropy (ΔS)
  • Familiarity with the concepts of reversible processes in thermodynamics
  • Basic calculus for manipulating logarithmic equations
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  • Study the derivation of the entropy change formula for ideal gases
  • Learn about the implications of reversible versus irreversible processes in thermodynamics
  • Explore the relationship between pressure, volume, and temperature in ideal gases
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Chase11
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Homework Statement


Four moles of an ideal gas expands at constant temperature until its pressure is reduced to half of its initial value. What is the change in entropy of the gas?


Homework Equations


ΔS=Q/T (For constant T) pinitial=p pfinal=.5p
Q=W
W=pdv
nrTln(vf/vi)


The Attempt at a Solution


I tried using nrTln(vf-vi), but realized I can't do that not knowing the temperature or the volumes. Is there an equation using deltap that I could use to solve for this that I am unaware of or can't figure out? Thanks
 
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Chase11 said:

Homework Statement


Four moles of an ideal gas expands at constant temperature until its pressure is reduced to half of its initial value. What is the change in entropy of the gas?


Homework Equations


ΔS=Q/T (For constant T) pinitial=p pfinal=.5p
Q=W
W=pdv
nrTln(vf/vi)


The Attempt at a Solution


I tried using nrTln(vf-vi), but realized I can't do that not knowing the temperature or the volumes. Is there an equation using deltap that I could use to solve for this that I am unaware of or can't figure out? Thanks
The problem statement says the the temperature is constant. So PV= constant. So, if you know the ratio of the initial and final pressures, you also know the ratio of the initial and final volumes. Please note also that you have implicitly assumed that the expansion is reversible.

Chet
 
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General formula for change in entropy is given as
S2 - S1 = CV[ln(T2 / T1) - ln(V2 / V1)] + CPln(V2/V1)
 

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