At what temperature is rms speed of air molecules double of that at NTP?

Question

At what temperature is rms speed of air molecules double of that at NTP? (A)  819° C  (B)  719° C  (C)  909° C  (D) None of these

Tardigrade Admin · Accepted Answer

crms propto √T Or crms propto √273 ..(i) Now consider that at temperature T', rms speed gets dubled, therefore 2(crms) propto √T' ... (ii) From Eqs. (i) and (ii), we get √(273/T')=(1/2) (273/T')=(1/4) T'=1092K=819° C

Q. At what temperature is rms speed of air molecules double of that at NTP?

$819^{\circ} C$

$719^{\circ} C$

$909^{\circ} C$

None of these

Q. At what temperature is rms speed of air molecules double of that at NTP?

819∘C

719∘C

909∘C

None of these

crms​∝T​ Or crms​∝273​ ..(i) Now consider that at temperature T′, rms speed gets dubled, therefore 2(crms​)∝T′​ ... (ii) From Eqs. (i) and (ii), we get T′273​​=21​ T′273​=41​ T′=1092K=819∘C

$819^{\circ} C$

$719^{\circ} C$

$909^{\circ} C$