Question

Following represents the Maxwell distribution curve for an ideal gas at two temperature $T_1$ and $T_2$. Which of the following option(s) are true?

• A. Total area under the two curves is independent of moles of gas
• B. $U_{mps}$ decreases as temperature decreases
• C. $T_1>T_2$ and hence higher the temperature, sharper the curve
• D. The fraction of molecules having speed $=U_{mps}$ decreases as temperature increases

Answer 1

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

$U_{mps}$ decreases as temperature decreases
The fraction of molecules having speed $=U_{mps}$ decreases as temperature increases
Total area under the two curves is independent of moles of gas

(A) Total area under the two curves is independent of moles of gas.
This is because, the quantity on the $Y$ axis includes the reciprocal of $N$.
Thus, the area under the curve gives fraction of molecules and total area is constant.
Hence, the option A is correct.
(B) $U_{mps}$ decreases as temperature decreases.Hence, the option B is correct.
(C) $T_1<T_2$ Hence, the option C is incorrect.
(D)As the temperature increases, the fraction of molecules with speed $U_{mps}$ decreases. Hence, the option D is correct.