Work in Adiabatic/ Isothermal and Piston

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SUMMARY

The discussion centers on comparing work done during adiabatic and isothermal processes in a piston containing oxygen, where the final volume is 1/4 of the initial and the temperature is 5 times greater. The participant derived expressions for work in both processes: Kln(vf/vi) for isothermal and -k(vf^(1-gamma) - vi^(1-gamma))/(1-gamma) for adiabatic. The conclusion drawn is that the work done in the isothermal process is greater than that in the adiabatic process, which can be visually confirmed by sketching the corresponding PV diagrams.

PREREQUISITES
  • Understanding of thermodynamic processes: adiabatic and isothermal
  • Familiarity with the ideal gas law and its applications
  • Knowledge of calculus, specifically integration techniques
  • Ability to interpret PV diagrams and thermodynamic cycles
NEXT STEPS
  • Study the derivation of work done in adiabatic processes using the first law of thermodynamics
  • Explore the concept of heat transfer in isothermal processes and its implications
  • Learn how to sketch and analyze PV diagrams for different thermodynamic processes
  • Investigate the impact of specific heat capacities on work done in various processes
USEFUL FOR

Students in thermodynamics, mechanical engineers, and anyone interested in understanding the principles of work done in gas processes.

~Sam~
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Homework Statement



Is work greater in adiabatic or isothermal process?

A piston with oxygen has a final volume 1/4 the initial. The temperature is also 5 times greater. Determine pressure change, heat released or absorbed, and work done on or by gas.

Homework Equations



the work for adiabatic and isothermal. General w= -integral pdv, conservation of energy deltaV=Q+w

The Attempt at a Solution



I have derived the the expressions for work in both adiabatic and isotherm process from their integrals. ie:- Kln(vf/vi) and -k(vf1-gamma-vi1-gamma)/(1-gamma). But I'm not sure how to show that work in isothermal > adiabatic.

For the second part I'm just not sure how to take into account both temperature and pressure, and I can't assume that it's adiabatic/isothermal in the beginning. Any ideas?

Note: I did trying doing the double integral, dvdt...but i still only get an expression only.
 
Last edited:
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Consider a gas undergoing an isothermal and an adiabatic change both having the same change in volume and both starting from the same point on a PV diagram.
Sketching the corresponding PV graphswill show which process has tha bigger work.
 

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