# Homework Help: Ideal gas law problem

1. Aug 29, 2014

### dk_ch

1. The problem statement, all variables and given/known data
for one mole of an ideal gas this relation holds good
P= P0 /{1+(V0/V)^2}, where P0and V0 are constants,
what will be its change in temperature in terms of P0,V0 and R,
if volume is doubled?

2. Relevant equations
for one mole of ideal gas we know PV=RT

Then RT/V= P0 /{1+(V0/V)^2}

How to proceed then? Can anyone help, please.

3. The attempt at a solution

Last edited: Aug 29, 2014
2. Aug 29, 2014

### CAF123

Evaluate the temperature of the gas when it occupies a volume V and 2V using the ideal gas law.

3. Aug 29, 2014

### dk_ch

The Answer given in the text is(11/10) P0V0/R. How shall I reach?

Last edited: Aug 29, 2014
4. Aug 29, 2014

### Staff: Mentor

According to the equation, if the initial volume is Vi, what is the initial pressure Pi? What is the initial temperature (using the ideal gas law? In terms of Vi, what is the final volume, Vf? What is the final pressure?

Chet

5. Aug 29, 2014

### dk_ch

If we take initial pressure P0
and initial volume as V0
Initial temp = T1
Final Pressure = P0 (remaining constant)
final doubled volume =2V0
and final temp = T2

then by ideal gas law for one mole of gas
T2-T1=2P0V0/R -P0V0/R=P0V0/R

Is this a correct solution? Then what is the utility of the given equation?

6. Aug 29, 2014

### Staff: Mentor

No. If V0 is the initial volume, then, from the equation they gave, P0 is not the initial pressure. As they said in the problem statement, P0 and V0 are just constants for the problem (and are not related to the initial conditions).

Chet

7. Aug 29, 2014

### dk_ch

for initial vol V0 the initial pressure is P0/2
for final vol 2V0 the final pressure is (4/5)P0
Then temperature change becomes =(11/10)P0V0/R

I think it is correct

8. Aug 29, 2014

### Staff: Mentor

Yes, if the initial volume is V0.

Chet

9. Sep 5, 2014

### dk_ch

Is it possible to arrive at the same result without having taken the initial volume as V0?
If possible please suggest a way out.

10. Sep 5, 2014

### Staff: Mentor

It might be. The problem statement sort of implies this. Have you tried, and, if so, how far have you gotten?

Chet

11. Sep 5, 2014

### dk_ch

I tried but failed to eliminate v1 initial volume to have the required relation. Please give hints if possible.

12. Sep 5, 2014

### Staff: Mentor

I'll give it a shot.

Chet

13. Sep 5, 2014

### Staff: Mentor

The only initial volume that matches the answer in the text is it is equal to Vo.

Chet

14. Sep 5, 2014

### dk_ch

So u have reached the same conclusion as I have , Thanks.