Question

The following graph represents the Maxwell distribution curve for an ideal gas at two temperatures $T_1$ and $T_2$. Which of the following option(s) is/are true?

• A. The total area under the two curves is independent of the number of moles of the gas.
• B. $U_{mp}$ decreases as the temperature decreases.
• C. $T_1>T_2$ and hence, higher the temperature, sharper the curve.
• D. The fraction of molecules that have speeds equal to $U_{mp}$ decreases as the temperature increases.

Answer 1

Answer: (A), (B), (D)

The correct options are
A The total area under the two curves is independent of the number of moles of the gas.
B $U_{mp}$ decreases as the temperature decreases.
D The fraction of molecules that have speeds equal to $U_{mp}$ decreases as the temperature increases.

$\Rightarrow$ Total area is independent of moles.
$\Rightarrow u_{mp}=\sqrt{\frac{2RT}{M}}\therefore$ decreases on reducing T.
$\Rightarrow u_{mp},<u_{m{p}_2}\therefore T_1<T_2$
$\Rightarrow$ Peak height $\left(\frac{dN}{Ndu}\right)$ decreases on increasing T. Hence fraction of molecules having $u_{mp}$ decreases at T increases.