# ISO processes question, help.

1. May 19, 2012

### charmedbeauty

1. The problem statement, all variables and given/known data

One mole of an ideal gas is contained in a cylinder with a movable piston. The initial pressure, volume, and temperature are P, V, and T, respectively. Consider each of the following processes:
· isobaric compression in which the final volume is one-half the initial volume
· isothermal compression in which the final pressure is two times the initial pressure
· isovolumetric process in which the final pressure is two times the initial pressure

Determine the work done on the gas for each process. (Use any variable or symbol stated above as necessary.):

isobaric compression:

Isothermal Compression:

Isovolumetric compression:

in In operational terms, match each process with its description of how to carry out the process.
isothermal
isovolumetric
isobaric

A. Put the cylinder into a refrigerator at absolute temperature T/2. Let the piston move freely as the gas cools.

B. With the gas in a constant-temperature bath at T, slowly push the piston in.

C. Lock the piston in place and hold the cylinder over a hotplate at 2T.

2. Relevant equations

3. The attempt at a solution

For Isobaric compression:

Constant pressure , also gas is being compressed so W is positive

so P(1/2)V.... since Vf is half Vi

for Isothermal compression:

gas is not under Cp. so evaluate the integral dW=-Pdv

W=-nRTln(1/2)P

and finally

Isovolumetric compression: w=0.

for part b matching the process to the right statement.

Isothermal:B

IsoVolumetric:C

IsoBaric: A

is this correct?

2. May 19, 2012

### Infinitum

All your approaches are correct Just a minute error, I found..

The initial pressure is P, the final pressure is 2P. So what is $ln(\frac{P}{2P})$?

3. May 19, 2012

### charmedbeauty

oops should be ln(1/2)

4. May 19, 2012

### charmedbeauty

are you sure this is right I put it in as nRTln(1/2) and it said it was wrong??

5. May 19, 2012

### Infinitum

You seem to be forgetting a negative sign.

6. May 19, 2012

### charmedbeauty

oops, thanks infinitum

7. May 19, 2012

### charmedbeauty

nope still wrong.

8. May 19, 2012

### Infinitum

It seems correct to me, maybe you need to give the value of ln(1/2) or base change it to 10 instead?

Edit : I just re-read the question....

Doh!

9. May 19, 2012

### charmedbeauty

oh so just get rid of n

10. May 19, 2012

### charmedbeauty

nope still wrong.

11. May 19, 2012

### Infinitum

This most definitely has to be the correct answer. Assuming you didn't forget the negative sign, I can't see anything wrong with it.

Did you try out putting in the value of ln(1/2) or changing the base to 10?