First Law of Thermodynamics - Isobaric Cooling

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SUMMARY

The discussion focuses on calculating the total work done during the thermodynamic process of an ideal monatomic gas transitioning through isothermal expansion and isobaric cooling. The initial conditions include a pressure of 3 atm, a volume of 1 L, and a temperature of 90 degrees Celsius. The user correctly identifies the need to apply the work equation w2→3=∫PdV and seeks clarification on determining the pressure at state 2 using the ideal gas law (P1V1=P2V2). The final state involves adiabatic compression back to the initial state, which is crucial for completing the work calculation.

PREREQUISITES
  • Understanding of the ideal gas law (PV=nRT)
  • Knowledge of thermodynamic processes: isothermal and isobaric
  • Familiarity with calculus, specifically integration for work calculations
  • Concept of adiabatic processes and their implications on pressure and volume
NEXT STEPS
  • Learn how to apply the ideal gas law in various thermodynamic processes
  • Study the derivation and application of the work done in isothermal and isobaric processes
  • Explore the concept of adiabatic processes and how they relate to work and energy conservation
  • Investigate the relationship between pressure, volume, and temperature changes in ideal gases
USEFUL FOR

Students studying thermodynamics, physics enthusiasts, and anyone involved in engineering disciplines focusing on gas laws and energy transformations.

chromium1387
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Homework Statement



An ideal monatomic gas has an initial pressure of 3 atm, an initial volume of 1 L, and is at an initial temperature of 90 degrees Celsius. It first expands isothermically to 2 L and is then cooled isobarically to a point where it is adiabatically compressed to its initial state. Calculate the total work done.

Homework Equations


w2→3=∫PdV=P(V2-V1


The Attempt at a Solution


Alright. I think I pretty much know what to do, but I am still a little confused. So, I've found the work done after the transition from state 1 to state 2. From there, can I calculate the new pressure at state 2 with P1V1=P2V2? And then, once I have my second pressure, this will be the pressure I use in my integral above. However, I do not know the volume the gas will be after the transition to the third state, which is what I need to find the value of the integral, correct? Or am I missing something?
 
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"...where it is adiabatically compressed to its initial state."
 

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