Question

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

• A. Total area under the two curves is independent of moles of gas
• B. If $d{U}_1=fUmp{s}_1$ & $d{U}_2=fUmp{s}_2$ then $A_1=A_2$
• C. $T_1>T_2$ and hence higher the temperature, sharper the curve.
• D. The fraction of molecules having speed $=$ Umps decreases as temperature increases.

Answer 1

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

The fraction of molecules having speed $=$ Umps decreases as temperature increases.
If $d{U}_1=fUmp{s}_1$ & $d{U}_2=fUmp{s}_2$ then $A_1=A_2$
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) The two areas are equal . 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 Umps decreases. Hence, the option D is correct.