# Constant internal energy with volume change?

Constant internal energy with volume change??

My book says that you can change the temperature of a substance at constant internal energy by changing only the volume.

how can this happen?

since the internal Energy E is this:
$\Delta$ E = q + w = q - P$\Delta$V

where q is heat, w is work, and V is volume

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In view of your degree I'm not sure at what level you are studying classical thermodynamics.

In particular you have stated an equation

Δ E = q + w = q - PΔV

Why have you reversed the work sign after the second equality?

i'm studying for the mcat....

my chemistry book has it reversed meaning that when the system does work, volume increases and there is a decrease in internal energy
and when work is done on the system, the volume decreases, so a double negative makes a positive and there is an increase in internal energy

So do you know the answer :-) ??

Forgive my british ignorance, Google tells me the mcat.. is an american medical exam.

Yes I asked because I really am trying to help, but there are many equations in thermodynamics and there is a philosophy to navigating through them.

First and foremost it is important to clearly define the boundaries of your system to which you are applying these equations.

Your equation is not helped by the two opposite sign conventions in use.

In general chemists consider energy out as negative and energy in as positive.

So they reckon heat added to the system and work done on the system as positive
similarly heat subtracted and work done by the system is negative.

They write the equation in the form Δ E = q + w

Historically mechanical engineers and physicists use a different convention.

They consider heat added to and work done by the system as positive.

Since any work done by the system reduces the internal energy they write the equation

Δ E = q - w

It is important to realise this when comparing formulae from different sources.

oh, i didn't know that...

all i know is that I don't understand how you can change the temperature of a substance at constant internal energy by changing only the volume :-(

is it a dumb question?

I'm getting dizzy switching between your threads here, can we deal with both at once?

yes!

OK taking the chemists version.

If Δ E = 0 then q = -w

So if q units of heat are added then -w units of work is done on the system (chemists convention).

But -w units of work on the system is the same as saying the system does w units of work on the rest of the universe.

To place this as an example this means that if we heat up a some air in an open container and allow it to expand freely into the atmosphere it the work it does on the rest of the universe in expanding exactly equals our heat input.

The heat input is given by Cp (the specific heat at constant pressure) times the amount of gas heated.
The work is the constant atmospheric pressure times the volume expansion Δ V.

As a less obvious example the expansion of a solid or liquid in free air is the same. Normally with a solid or liquid we only have Cp we do not also have Cv as with a gas.

The answer to your other question is the reason that enthalpy (or heat content) was introduced. Have you come across enthalpy?

youre talking about heat engines right? I guess i was confused bc i thought that temperature is proportional to internal energy so that when you increase temperature it reflects an increase in internal energy
thats why the statement is kind of weird

oh yeah and concerning the other question, i had completely forgotten about entropy!