How Do State Functions Apply to a Multi-Step Thermodynamic Process?

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SUMMARY

The discussion focuses on the application of state functions in a multi-step thermodynamic process involving a monatomic ideal gas. The process consists of four reversible steps: free expansion into a vacuum, heating at constant volume, adiabatic expansion, and isobaric heating. The key conclusion is that for state functions like internal energy (U), entropy (S_sys), and enthalpy (H), the total change can be calculated by comparing the initial and final states, specifically by taking the values from step 4 and subtracting those from step 1. The participants clarify that the change in U for the first step is zero, while the fourth step yields a nonzero value, reinforcing that state functions depend solely on the initial and final states, not the path taken.

PREREQUISITES
  • Understanding of thermodynamic state functions (U, S, H)
  • Knowledge of ideal gas laws and behavior
  • Familiarity with reversible and irreversible processes
  • Basic principles of adiabatic and isobaric processes
NEXT STEPS
  • Study the implications of state functions in thermodynamic cycles
  • Learn about the differences between reversible and irreversible processes in thermodynamics
  • Explore the concept of adiabatic processes in greater detail
  • Investigate the mathematical formulations for calculating changes in state functions
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This discussion is beneficial for thermodynamics students, educators, and professionals who seek to deepen their understanding of state functions and their application in multi-step processes involving ideal gases.

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Thermodynamics question -- please help

A monatomic, ideal gas undergoes 4 steps, all reversible

1) At initially 293 K and 1 atm, it is let freely expand into a vacuum, tripling the volume.
2) It is then heated to 393 K, keeping V constant.
3) It is then let expand adiabatically, doubling the volume.
4) It is then warmed up to 293 K in an isobaric manner.

-----

To calculate the total change in U, S_sys, and H values do I add the values for each step or just take step 4 minus step 1? I realize they are state functions, but this isn't a chemical reaction per se, just a series of physical processes. Plus, the change in U for #1 is zero, and for #4 it is nonzero. I assume that even though U is a state function, I don't take change in U for #4 minus change in U for #1 since that would not be zero. Since the temperature is the same, it is isothermic and ideal and therefore the change in U must be zero. Thus, adding the state function values for each step results in what I imagine is the correct answer. Is this correct? I'm not sure about the line of reasoning so I'd appreciate some help...
 
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A state function is a state function; you can look at the end value only (compare #4 to #1) or move from #1 to #4 step by step. What would be the problem with a nonzero change in U?

By the way, it's a contradiction to describe #1 as reversible. Reversible means, among other things, that the pressure on the other side of an expanding boundary is equal. Free expansion into a vacuum is irreversible.
 

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