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

[stuffchemistry]

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 = δq_rev + δw_rev.

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...

 

[Andrew Mason]

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 = δq_rev + δw_rev.

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