Enthelpy's Equation of state vs Energy's equation of state

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SUMMARY

The discussion centers on the confusion surrounding the equations of state for energy and entropy, specifically the relationships between enthalpy (H), internal energy (U), and pressure-volume work (PV). The established equation H = U + PV leads to the differential form dH = dU + PdV + VdP. Participants clarify that U = q + PV is not an equation of state because q and work (W) are path-dependent and not state functions, while PV is a state function. The first law of thermodynamics is expressed as dU = δQ - δW, emphasizing that the differential form describes processes rather than states.

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  • Understanding of thermodynamic concepts such as internal energy (U) and enthalpy (H).
  • Familiarity with the first law of thermodynamics and its differential forms.
  • Knowledge of state functions versus path-dependent functions in thermodynamics.
  • Basic grasp of pressure-volume work (PV) and its role in thermodynamic equations.
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  • Study the first law of thermodynamics in detail, focusing on its implications for energy changes.
  • Learn about state functions and path functions in thermodynamics to clarify their differences.
  • Explore the ideal gas law (PV = nRT) as a classic example of an equation of state.
  • Investigate the concept of quasi-static processes and their significance in thermodynamic analysis.
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stuffchemistry
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I'm really confused about Energy and Entropy's equations of state, and how their differentials work.

So I find everywhere that H = U + PV. And so dH = d(U +PV) = dU + PdV + VdP
Ok, that makes sense. But then I look at energy and try to get the equation of state

dU = δqrev + δwrev.

That also makes sense. But what is the equation of state for just U itself? Why is U = q + PV not an equation of state? Why is only the differential the equation of state? How come you can't take the differential of U = q + PV to get dU = dq + PdV + VdP?

Is the equation of state for energy just U = H - PV, rearranging H = U + PV?
I'm really lost in this...
 
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stuffchemistry said:
I'm really confused about Energy and Entropy's equations of state, and how their differentials work.

So I find everywhere that H = U + PV. And so dH = d(U +PV) = dU + PdV + VdP
Ok, that makes sense. But then I look at energy and try to get the equation of state

dU = δqrev + δwrev.

That also makes sense. But what is the equation of state for just U itself? Why is U = q + PV not an equation of state? Why is only the differential the equation of state? How come you can't take the differential of U = q + PV to get dU = dq + PdV + VdP?
Welcome to PF, stuffchemistry!

q and W are not state functions ie. their values do not depend on the state of the system. Rather they depend on the process or path followed in moving between equilibrium states. The differential form (first law) is not a relation of states either. It describes the measure of physical quantities in a process between states, not the states themselves.

PV is a state function. However, dU = δQ-PdV is not necessarily true. The first law is dU = δQ-δW. δW = PdV only if the external and internal pressures are the same (ie. the process is quasi-static).

Is the equation of state for energy just U = H - PV, rearranging H = U + PV?
I'm really lost in this...
An equation of state usually relates parameters that fully describe the thermodynamic state of a system, eg. PV=nRT is the equation of state of an ideal gas. How are you defining the term "equation of state"?

AM
 
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