Thermodynamics work done formula

[scott harvey]

Hi all
i was wondering if any one could help with this question. i can do the calculations just need to see the formula and how it is set out the material i was sent to help me has nothing to do with this type of question.

 

In a closed system 0.3kg of gas at 373 k is expanded isothermally and reversibly from 1MPA pressure to 200 KPA. given that Cv = 718 J/kg K and R = 287 J/kg K determine:

the work done.

the state of energy transfer within this isothermal process explaining your answer.

 

many thanks

 

scott

[swansont]

You have to show what you've done so far. What's changing and what's not changing in an isothermal process?

[studiot]

If you can do the 'calculations', why do you 'need the formulae' ?

 

Which formulae?

 

As I see it, this question is testing your understanding, not your arithmetic so explain what is happening.

[scott harvey]

I should of worded my question better, i have not attempted this question as i am searching for an example of it. i don't understand how to determine work done in general, i do not know where to begin with the question.

 

sorry if this is a bit of a cheek

[studiot]

So start by following swansont's advice.

 

Actually this is good advice for all physics questions
(He was a physics teacher after all)

 

List what you know.

 

Then list a few things you don't know, but might like to.

 

So

 

What is a closed system, why did they specify one?

 

If the question also specifies work can pass the boundary, what else can and can't?

 

What formulae do you know connecting these things?

 

I am going to cut the grass now, but I will look in for a cup of tea and to see how you are getting on, from time to time.

Edited April 6, 2015 by studiot

[scott harvey]

This is what i have come up with to solve the work done part

[studiot]

Since when did they start measuring volume in kilograms?

 

Why can you not simply answer the questions swansont and I asked?

 

They are very simple and very basic and will lead you to the correct answers.

Edited April 6, 2015 by studiot

[swansont]

You aren't given the volume. Do you have an equation that relates volume to other terms that you know?

 

What is n in that equation?

[studiot]

Here is a hint.

 

This question is about the first law of thermodynamics.

 

Can you at least state what that is so we can take it further?

[scott harvey]

yeah i can do that, the first law states that energy can neither be created nor destroyed, thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than the creation of energy from nothing

[studiot]

yeah i can do that, the first law states that energy can neither be created nor destroyed, thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than the creation of energy from nothing

 

 

 

Does it?

 

I thought it stated that

 

the change in internal energy = the sum of the work done and the heat exchanged

 

dU = q + w or dU = q - w, depending upon your sign convention.

 

Can we discuss the problem in these terms since that is what your lecturers are expecting?

[scott harvey]

what i wrote is what is stated on the material that was given to me to help with the course, i have asked my tutor to explain and all he has given me is this formula W = -m RT ln P1/

P2

if you don't wish to continue that's fine. i understand im coming across vague and doing thin completely different to what you ask. im new to this and this question has stomped me

 

yes we can discuss in them terms, i somewhat understand.

[swansont]

what i wrote is what is stated on the material that was given to me to help with the course, i have asked my tutor to explain and all he has given me is this formula W = -m RT ln P1/ [/size]

P2[/size]

if you don't wish to continue that's fine. i understand im coming across vague and doing thin completely different to what you ask. im new to this and this question has stomped me

Do you know where that equation comes from?

 

Also, do you see how your statement of the 1st law and studiot's say the same basic thing, except one is in much more detail?

[scott harvey]

an isothermal gas expansion when the gas expansion follows the law pV1 = C

[studiot]

The question also told you that

 

 

Scott Harvey

Cv = 718 J/kg K and R = 287 J/kg K determine:

 

But you have made no attempt to use this information.

 

So I'm quite sure that either your lecturers or your tutor gave you much more information than you seem willing to let on.

 

Yes the equation you quote (from your lecturer) is appropriate, but only when you understand what you are doing and we have some way to go to reach that stage.

 

So just please try to answer my simple questions and swansont's and don't offer any additional information.

 

This trail will eventually lead to the answer you need.

Edited April 6, 2015 by studiot

[scott harvey]

i can only tell you what i have in front of me that's the question.

 

 

 

forgetting that i will try and answer your question, please list them

 

[studiot]

Was it so long ago?

 

 

I asked you what an open system was.

 

Swansont asked you what isothermal meant.

 

Both are mentioned in your set question.

Edited April 6, 2015 by studiot

[scott harvey]

you haven't got to be like that mate

 

a closed system can exchange heat or work with its surroundings

 

isothermal is a process or change taking place at constant temperature

[studiot]

 

scott harvey

a closed system can exchange heat or work with its surroundings

 

isothermal is a process or change taking place at constant temperature

 

 

Both right.

 

Just to add the system is closed because no matter (mass ) leaves or enters.

 

So work and/or heat are exchanged with the surroundings and our goal is to evaluate each, bearing in mind that these exchanges take place at constant temperature.

 

We are told that the gas expands

 

So what changes and which way is any work 'exchanged' ie what does work on what?

 

Once that is decided we can find a formula to calculate the value of that work, if any.

 

If we expanded a gas what would normally happen to the temperature of that gas?

[scott harvey]

would that be an exchange of pressure for temperature ?

 

if we expand a gas it would increase the temperature ?

[studiot]

We are assuming an ideal gas.

 

Which brings us to the dreaded first law and internal energy.

 

The internal energy of an ideal gas depends only upon the temperature.

 

At the very beginning, swansont asked you what isothermal means.

 

So what are the implications of this being an isothermal process?

[swansont]

We are assuming an ideal gas.

 

 

Should we be assuming this? C_v for an ideal gas is 3/2 R, and for a gas with n degrees of freedom it's n/2 R. The information tells us we have a diatomic gas. (Though thermo was along time ago, so I don't recall offhand whether this matters for an isothermal process)

 

edit: I can't think of a reason why we would care if it's monoatomic or not for this problem. We have PV = constant, and that should be enough to solve it.

[studiot]

The point is that if the internal energy depends only upon temperature and temperature does not change then the internal energy does not change.

 

That is dU = 0.

 

That is q = -w = RT ln(V₂/V₁) = RT ln(P₁/P₂)

 

Which is an expanded version of the formula scott's tutor provided.

Edited April 8, 2015 by studiot

[swansont]

The point is that if the internal energy depends only upon temperature and temperature does not change then the internal energy does not change.

 

That is dU = 0.

 

That is q = -w = RT ln(V₂/V₁) = RT ln(P₁/P₂)

 

Which is an expanded version of the formula scott's tutor provided.

 

Right.

 

He should see where the formula comes from.

[studiot]

Furthermore , R, C_v and the quantity of gas are all given in engineer's units (kg- somethings) so n is not needed.