Consider an ideal gas with the following distribution of speeds

Home » Consider an ideal gas with the following distribution of speeds

Consider an ideal gas with the following distribution of speeds

a) calculate Vrms and hence T (m = 3.0 × 10^-26 kg)

b) if all the molecules with speed 1000 m/s escape from the system, calculate new V_rms and hence T

Answer:

a)

$V_{rms}^{2}=\frac{\sum\limits_{i}{{{n}_{i}}v_{i}^{2}}}{\sum{{{n}_{i}}}}$

$V_{rms}^{2}=\frac{10\times {{(200)}^{2}}+20\times {{(400)}^{2}}+40\times {{(600)}^{2}}+20\times {{(800)}^{2}}+10\times {{(1000)}^{2}}}{100}$

$V_{rms}^{2}=408000$

${{V}_{rms}}=639m/s$

$\frac{1}{2}m{{V}^{2}}_{rms}=\frac{3}{2}kT$

$\therefore T=\frac{1}{3}\frac{mv_{rms}^{2}}{k}=\frac{1}{3}\times \frac{3.0\times {{10}^{-26}}\times 4.08\times {{10}^{5}}}{1.38\times {{10}^{-23}}}$

$T=296K$

(b) $V_{rms}^{2}=\frac{10\times {{(200)}^{2}}+20\times {{(400)}^{2}}+40\times {{(600)}^{2}}+20\times {{(800)}^{2}}}{100}$

$V_{rms}^{2}=342000$

${{V}_{rms}}=584m/s$

$T=\frac{1}{3}\frac{mV_{rms}^{2}}{k}=248K$

i

Sign up now and study all subjects for free