Adiabatic Expansion Homework: q,w,ΔU,ΔT,ΔH

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SUMMARY

The discussion focuses on calculating thermodynamic properties during the adiabatic expansion of 2.5 mol of O2 gas. The initial conditions include a volume of 23 dm³ and a temperature of 270 K, with the gas expanding against a constant pressure of 600 Torr until the volume increases by a factor of 3.0. Key equations used include Tf=Ti(Vi/Vf)^(1/c) and the relationship between heat capacities, Cv,m=Cp,m-R. The user successfully calculated q, w, and ΔU but struggled with determining the temperature change (ΔT) due to confusion over the correct expression for Cv,m.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically adiabatic processes.
  • Familiarity with the ideal gas law and its applications.
  • Knowledge of heat capacities, including Cp,m and Cv,m.
  • Basic algebra and calculus skills for manipulating thermodynamic equations.
NEXT STEPS
  • Review the derivation of the equation Tf=Ti(Vi/Vf)^(1/c) for adiabatic processes.
  • Study the relationship between heat capacities, specifically how to derive Cv,m from Cp,m.
  • Learn about the first law of thermodynamics as it applies to adiabatic processes.
  • Explore examples of calculating ΔT in adiabatic expansions using real gas data.
USEFUL FOR

Students studying thermodynamics, particularly those tackling adiabatic processes in physical chemistry or engineering courses.

smithnh
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Homework Statement



A sample of 2.5 mol O2 (Cp,m = 29.355 J K-1 mol-1) is originally confined in 23 dm3 at 270 K and then undergoes adiabatic expansion against a constant pressure of 600 Torr until the volume has increased by a factor of 3.0. Calculate q, w, ΔU, ΔT, and ΔH. (The final pressure of the gas is not necessarily 600 Torr.)

Homework Equations



Tf=Ti(Vi/Vf)^(1/c); c=Cv,m/R; Cv,m=Cp,m-R

The Attempt at a Solution



I have found q,w, and the change in internal energy, however I am having difficulty finding the temperature change. Why is my approach not working.

Tf=270K*(23 dm^3/ 69 dm^3)^(8.314 J/mol/K /(29.355 J/mol/k- 8.314 J/mol/K)

Is it that the heat capacity at constant volume is not Cp,m-R and if so how do I find it.
 
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I think you got to find delta T by using W=C(at constant volume) * delta T, where
C(at constant pressure)- C(at constant volume)= nR
 

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