Adiabatic Expansion of a Gas: Final Pressure-Volume Product Calculation

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SUMMARY

The discussion centers on the adiabatic expansion of a diatomic gas, specifically calculating the final pressure-volume (PV) product after performing 101J of work. The initial conditions include a pressure of 365Pa and a volume of 70m³, with the degrees of freedom determined to be 3, leading to a heat capacity ratio (γ) of 1.4. The equation used for the calculation is W = (1/γ-1)(pfvf - pivi), resulting in a final PV product of 25590 Pa·m³. The calculations were confirmed to be correct, addressing concerns about the degrees of freedom for diatomic versus monatomic gases.

PREREQUISITES
  • Understanding of adiabatic processes in thermodynamics
  • Familiarity with the concepts of pressure, volume, and work
  • Knowledge of degrees of freedom for diatomic and monatomic gases
  • Proficiency in using the equation W = (1/γ-1)(pfvf - pivi)
NEXT STEPS
  • Study the derivation and implications of the adiabatic process equations
  • Learn about the differences in degrees of freedom between diatomic and monatomic gases
  • Explore practical applications of the PV product in real-world thermodynamic systems
  • Investigate the effects of varying work done on the final state of a gas during adiabatic expansion
USEFUL FOR

Students and professionals in physics and engineering, particularly those focused on thermodynamics and gas laws, will benefit from this discussion.

vetgirl1990
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Homework Statement


A gas consisting of diatomic molecules that can rotate but not oscillate at a given range of temperatures expands adiabatically from pressure of 365Pa and volume of 70m3, doing 101J of work, while expanding to a final volume. What is its final PV (pressure volume) product?

Homework Equations


For an adiabatic expansion:
W = (1/ϒ-1)(pfvf - pivi)

The Attempt at a Solution


i) Degrees of freedom: 3
Therefore, ϒ=1.4

ii) Plug and chug of the equation above.
W = (1/ϒ-1)(pfvf - pivi)
101 = (1/1.4-1)(pfvf - 365*70)
101 = 2.5pfvf - 63875
pfvf = 25590 Pa / m3

I'm fairly certain I found the degrees of freedom correctly, and the latter part of my calculations is pretty straightforward... Still getting the wrong answer, however. Chance that the answer is wrong? Or am I approaching the problem incorrectly?
 
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Isn't it 3 degrees of freedom for a monatomic gas?
 

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