Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 16 - A Macroscopic Description of Matter - Exercises and Problems - Page 465: 44

Answer

$\approx 10\;\rm g$

Work Step by Step

We know, for an ideal gas, that $$PV=nRT$$ where $n=m/M_{\rm Ne}$ whereas $M_{\rm Ne}$ is the atomic mass of the neon. Hence, $$PV=\dfrac{m}{M_{\rm Ne}}RT$$ Hence, $$P=\left(\dfrac{mR}{M_{\rm Ne}V} \right)T$$ The term between parenthesis is the slope of the $P {\rm -versus-} T$ function. $${\rm Slope}=\dfrac{mR}{M_{\rm Ne}V} $$ Solving for $m$; $$m=\dfrac{M_{\rm Ne}V\;{\rm Slope}} { R}$$ Plugging the known; $$\boxed{m=\dfrac{(20.2)(2\times 10^{-3})\;{\rm Slope}} { (8.31)}}$$ So we need to draw the best-fit line of $P$ versus $T$ and then find the slope. We have to convert the given temperature data to Kelvin and the given gauge pressure to absolute pressure (by adding 1 atm to the gauge pressure) in Si units of Pascal. \begin{array}{|c|c| } \hline T{\;(\rm K})& P{\;(\rm Pa}) \\ \hline 373 & 7.62\times 10^5 \\ \hline 423 & 8.92\times 10^5 \\ \hline 473 & 9.96\times 10^5 \\ \hline 523 &1.073 \times 10^6 \\ \hline \end{array} Now we need to plug these dots into a $P$-$T$ graph and then draw the best-fit line that connects them and then find the slope of this line. You can use any software calculator. Plugging the slope from the figure below into the boxed formula above, $$ m=\dfrac{(20.2)(2\times 10^{-3}) (2074)} { (8.31)} $$ $$m=\color{red}{\bf10.08}\;\rm g$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.