Pressure at Height: Calculate Pressure Change

[Saitama]

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:
p=p_0exp\left(\frac{-Mgh}{RT_0}\right)

 

[ehild]

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:
p=p_0exp\left(\frac{-Mgh}{RT_0}\right)

Why not?

ehild

 

[Saitama]

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 $\exp\left({-\frac{Mgh}{RT}}\right)=x$.
\frac{p_0-p_{20}}{p_0-p_{10}}-2=\frac{1-x^2}{1-x}-2
=(1+x)-2=x-1

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 $T=293 K$.

 

[ehild]

What is the molar mass of nitrogen gas?

ehild

 

[Saitama]

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?

 

[ehild]

Correct.

ehild

 

[Saitama]

Correct.

ehild

But when I submit this, it is marked incorrect. :(

 

[ehild]

Try more digits.

 

[Saitama]

Try more digits.

Thanks a bunch, yes, it was a problem with significant digits. :)