Understanding \DeltaH and \DeltaE in Constant Volume Process

[phymatter]

What is the difference between \DeltaH and \DeltaE in a constant volume process ?

 

[Gerenuk]

By definition it is always true that
<br /> H=E+pV<br />
At constant volume you have
<br /> \Delta_V H=\Delta E+V\Delta p<br />
Here you see the difference in the term.
What exactly did you want to know?

 

[jeedoubts]

but acc to first law Heat supplied = internal energy + work done
i.e.
i.e. \Deltah = \DeltaU + \DeltaW
and \DeltaW = \Delta(pv) and
\Delta(pv) = P\DeltaV + V\DeltaP and
for work done V\Deltap is taken as zero so how come can we say here V\DeltaP is not taken as zero here?

 

[Mapes]

i.e. \Deltah = \DeltaU + \DeltaW
and \DeltaW = \Delta(pv)

Hi jeedoubts, welcome to PF. Can you give a reference for these two equations? I doubt very much that they're correct. For example, work is defined as P\Delta V, not \Delta(PV).

I agree with Gerenuk's answer.

 

[jeedoubts]

what does the quantity v\Deltap refers to then?

 

[Mapes]

The difference between enthalpy change and energy change in a constant-volume process.

 

[jeedoubts]

physically what does it represent??

 

[Mapes]

I don't know of a simpler description (other than the literal "volume multiplied by pressure change"). What are you looking for?

 

[Gerenuk]

\DeltaW = \Delta(pv) and
\Delta(pv) = P\DeltaV + V\DeltaP

Neither equation is correct in general. The correct equations are
<br /> \mathrm{d}W=p\mathrm{d}V<br />
(or with the other sign if you consider the work done on the system) and if you wish
<br /> \mathrm{d}(pV)=p\mathrm{d}V+V\mathrm{d}p<br />
It follows that only for constant volume or constant pressure processes the work can be described by
<br /> W=p\Delta V\qquad\text{(const. p or const. V)}<br />
Is it very important to know what is the general equation and what the special case. These special cases only apply if the conditions are met.

Mapes is correct.