# 1st law of thermo

## Main Question or Discussion Point

What is the difference between $$\Delta$$H and $$\Delta$$E in a constant volume process ?????

## Answers and Replies

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

but acc to first law Heat supplied = internal energy + work done
i.e.
i.e. $$\Delta$$h = $$\Delta$$U + $$\Delta$$W
and $$\Delta$$W = $$\Delta$$(pv) and
$$\Delta$$(pv) = P$$\Delta$$V + V$$\Delta$$P and
for work done V$$\Delta$$p is taken as zero so how come can we say here V$$\Delta$$P is not taken as zero here?

Mapes
Homework Helper
Gold Member
i.e. $$\Delta$$h = $$\Delta$$U + $$\Delta$$W
and $$\Delta$$W = $$\Delta$$(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.

what does the quantity v$$\Delta$$p refers to then????

Mapes
Homework Helper
Gold Member
The difference between enthalpy change and energy change in a constant-volume process.

physically what does it represent??

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

$$\Delta$$W = $$\Delta$$(pv) and
$$\Delta$$(pv) = P$$\Delta$$V + V$$\Delta$$P
Neither equation is correct in general. The correct equations are
$$\mathrm{d}W=p\mathrm{d}V$$
(or with the other sign if you consider the work done on the system) and if you wish
$$\mathrm{d}(pV)=p\mathrm{d}V+V\mathrm{d}p$$
It follows that only for constant volume or constant pressure processes the work can be described by
$$W=p\Delta V\qquad\text{(const. p or const. V)}$$
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.