Calculating Work Done by Ideal Gas: Qualitative Pressure vs Volume

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SUMMARY

The work done by 1 mole of an ideal gas during adiabatic expansion from volume V_1 to V_2 can be calculated using the formula W = -∫(p dV), where p is the pressure as a function of volume. In this scenario, if the final volume V_2 is less than the initial volume V_1, the work done is negative, indicating that work is performed on the gas. A qualitative graph of pressure changes as a function of volume, p = p(V), illustrates this relationship effectively.

PREREQUISITES
  • Understanding of ideal gas laws
  • Familiarity with adiabatic processes
  • Knowledge of calculus, specifically integration
  • Ability to interpret pressure-volume (p-V) diagrams
NEXT STEPS
  • Study the derivation of the work done in adiabatic processes
  • Learn about the ideal gas law and its applications
  • Explore pressure-volume (p-V) diagrams for different thermodynamic processes
  • Investigate the concept of internal energy changes in ideal gases
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Students and professionals in thermodynamics, physics enthusiasts, and anyone studying the behavior of gases under varying pressure and volume conditions.

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1. Calculate the work done by 1 mole of ideal gas in expanding adiabatically from V_1 to V_2 (volumes). Make a qualitative figure of pressure changes as a function volume changes p=p(V).

I will be very grateful for solving this problem because I spent so much time on it and I still do not know how to do it.
Thank you in advance!
 
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adiab2.gif


The work done by the gas can then be determined. If the final volume is less than the initial, then work is done on the gas and the work will be negative.

wadi.gif
 

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