• Support PF! Buy your school textbooks, materials and every day products Here!

Pressure at a height

  • Thread starter Saitama
  • Start date
  • #1
3,812
92

Homework Statement


(see attachment)


Homework Equations





The Attempt at a Solution


I am not sure how to start with this problem. Do I need to use the barometric formula?

Barometric formula:
[tex]p=p_0exp\left(\frac{-Mgh}{RT_0}\right)[/tex]
 

Attachments

Answers and Replies

  • #2
ehild
Homework Helper
15,492
1,874

Homework Statement


(see attachment)


Homework Equations





The Attempt at a Solution


I am not sure how to start with this problem. Do I need to use the barometric formula?

Barometric formula:
[tex]p=p_0exp\left(\frac{-Mgh}{RT_0}\right)[/tex]
Why not?

ehild
 
  • #3
3,812
92
Why not?

ehild
I tried that but it gives me the wrong answer.
Here's my attempt:

Let h=10m, then 2h=20m.
##p_{20}=p_0 \exp\left({-\frac{Mg(2h)}{RT}}\right)##
##p_{10}=p_0 \exp\left({-\frac{Mgh}{RT}}\right)##

Let ##\exp\left({-\frac{Mgh}{RT}}\right)=x##.
[tex]\frac{p_0-p_{20}}{p_0-p_{10}}-2=\frac{1-x^2}{1-x}-2[/tex]
[tex]=(1+x)-2=x-1[/tex]

When I substitute the values of all the variable in exponential term, I get ##x-1=-5.6 \times 10^{-4}## but this is wrong. :(

I used ##M=14 \times 10^{-3} kg/mol##, ##R=8.314 J/(mol \cdot K)## and ##T=293 K##.
 
  • #4
ehild
Homework Helper
15,492
1,874
What is the molar mass of nitrogen gas?

ehild
 
  • #5
3,812
92
What is the molar mass of nitrogen gas?

ehild
Woops, its 28, thanks! :)

This time I get: ##-1.1 \times 10^{-3}##, is this right?
 
  • #6
ehild
Homework Helper
15,492
1,874
Correct.

ehild
 
  • #7
3,812
92
Correct.

ehild
But when I submit this, it is marked incorrect. :(
 
  • #8
ehild
Homework Helper
15,492
1,874
Try more digits.
 
  • #9
3,812
92
Try more digits.
Thanks a bunch, yes, it was a problem with significant digits. :)
 

Related Threads on Pressure at a height

  • Last Post
Replies
2
Views
4K
Replies
6
Views
8K
  • Last Post
Replies
11
Views
2K
Replies
4
Views
782
  • Last Post
Replies
2
Views
7K
Replies
3
Views
13K
  • Last Post
Replies
21
Views
10K
Replies
1
Views
3K
Top