Enthelpy of Reaction under Constant Volume?

[Hereformore]

Homework Statement

So we know Enthalpy under constant Pressure and Internal Energy under Constant Volume. By

H = U + dPdV

U= I + W

W= -PdV

under Isobaric conditions

H = I -PdV + dPdV
= U

Enthalpy = Internal Energy
_________________________________________
Under Isochoric Conditions
W= O because change in V =o

so U = q + 0
Internal Energy = q

But wouldn't Enthalpy also = q under constant volume since dPdV = 0 as well if volume isn't changing?

Homework Equations

H = U + dPdV

U= I + W

W= -PdV

The Attempt at a Solution

( Outlined above)

Am i confusing the dPdV specific to enthalpy and PdV in work?

 

[rude man]

Looks confusing. what's the question?

H = U + PV so dH = dU + pdV + Vdp
dH = dU + Vdp under isochoric
but dU = dQ - pdV = dQ under isochoric
so dH = dQ + Vdp under isochoric.

Is that something like what you're looking for?

 

[Hereformore]

Looks confusing. what's the question?

H = U + PV so dH = dU + pdV + Vdp
dH = dU + Vdp under isochoric
but dU = dQ - pdV = dQ under isochoric
so dH = dQ + Vdp under isochoric.

Is that something like what you're looking for?

Yeah. I see. So Enthalpy = Internal Energy + Change in Pressure times volume.
While change in internal energy (dU) = q + Change in Volume times pressure.

is this correct?

 

[rude man]

Yeah. I see. So Enthalpy = Internal Energy + Change in Pressure times volume.
While change in internal energy (dU) = q + Change in Volume times pressure.

is this correct?

enthalpy = internal energy plus pressure times volume ... basic statement, always true
change in internal energy = heat added minus pressure times change in volume. "Change" should read "differential change". To get change you integrate differential changes.

 

[HalfLostAndSearching]

No, you are not confusing the two. The dPdV in the equation for enthalpy (H = U + dPdV) represents the change in pressure and volume at constant temperature, whereas the PdV in the equation for work (W = -PdV) represents the work done on or by the system due to a change in volume. In the equation for enthalpy, dPdV can also be written as dPV because pressure and volume are inversely proportional at constant temperature. Therefore, in a constant volume process, dPdV (or dPV) is equal to zero, but the PdV in the work equation is not. This is why enthalpy and internal energy are equal under constant volume, but the work done is not necessarily zero.