Question

If two gases 'A' & 'B' at temperatures $T_A\&T_B$ respectively have identical Maxwellian plots, then which of the following statements are true?

• A. $T_B=T_A$
• B. $M_B=M_A$
• C. $\frac{T_A}{T_B}=\frac{M_B}{M_A}$
• D. Gases A and B may be $O_2$ and $S{O}_2$ at ${27}^{o}C$ and ${327}^{o}C$ respectively.

Answer 1

Answer: (C), (D)

Gases A and B may be $O_2$ and $S{O}_2$ at ${27}^{o}C$ and ${327}^{o}C$ respectively.
$\frac{T_A}{T_B}=\frac{M_B}{M_A}$

For identical Maxwellian plots, the root mean square velocity for both the gases should be equal.

$\sqrt{\frac{3R{T}_A}{M_A}}=\sqrt{\frac{3R{T}_B}{M_B}}$

$\therefore \frac{T_A}{T_B}=\frac{M_B}{M_A}$

For $O_2$ at ${27}^{o}C$, $V_{rms}=\sqrt{\frac{900R}{32}}$

For $S{O}_2$ at ${327}^{o}C$, $V_{rms}=\sqrt{\frac{1800R}{64}}=\sqrt{\frac{900R}{32}}$

Thus the gases A and B can be $O_2$ and $S{O}_2$ at ${27}^{o}C$ and ${327}^{o}C$ respectively.