Change in entropy for adiabatic compression

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SUMMARY

The discussion focuses on calculating the change in entropy for adiabatic compression of nitrogen gas, specifically 8.02 x 10^-1 moles at initial conditions of 2 x 10^-2 m³, 1 x 10^5 Pa, and 300 K. The relevant equations include S2-S1 = Cv ln(P2/P1) + Cp ln(V2/V1) and the ideal gas law PV = nRT. The challenge lies in determining the change in pressure during adiabatic compression, which requires applying the relationship defined by the adiabatic condition using the specific heat ratio (\gamma = 1.4).

PREREQUISITES
  • Understanding of the ideal gas law (PV = nRT)
  • Knowledge of specific heat capacities (Cv and Cp) for nitrogen gas
  • Familiarity with adiabatic processes and the concept of \gamma
  • Basic calculus for logarithmic functions
NEXT STEPS
  • Study the derivation of the adiabatic condition for ideal gases
  • Learn how to calculate Cv and Cp for different gases
  • Explore the implications of the ideal gas law in non-constant temperature scenarios
  • Investigate the relationship between pressure, volume, and temperature during adiabatic processes
USEFUL FOR

This discussion is beneficial for students in thermodynamics, particularly those studying gas laws and adiabatic processes, as well as professionals in engineering fields dealing with thermodynamic systems.

Bugsy23
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Homework Statement



A sample of 8.02*10^-1 moles of nitrogen gas ([tex]\gamma[/tex]=1.4) occupies a volume of 2*10^-2m^3 at pressure 1*10^5pa and temperature 300K. The gas is adiabatically compressed to half its original volume. What is the change in entropy of the gas?


Homework Equations



S2-S1=CvIn(P2/P1)+CpIn(V2/V1)

PV=nRT

The Attempt at a Solution



I have already worked out the values for Cv and Cp and the change in volume of the gas, but I don't know how to find the change in pressure. Since nitrogen behaves as an ideal gas, it should be possible to find it using PV=nRT, but that also requires knowing the change in temperature. Is there a different way of working out the change in pressure?
 
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You have to use the adiabatic condition. This condition shows the relationship between P and V in an adiabatic change. Hint: it uses [itex]\gamma[/itex]

AM
 

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