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The temperature of an ideal gas is incre...

The temperature of an ideal gas is increased from `27 ^@ C` to `927^(@)C`. The rms speed of its molecules becomes.

A

`sqrt((927)/(27))` times of the earlier value

B

same as before

C

halved

D

doubled

Text Solution

Verified by Experts

The correct Answer is:
D
Root mean square velocity at `T_(1)` temperature,
`U_(1)=sqrt((3RT_(2))/(M))=sqrt((3R(27+273))/(M))" ...(i)"`
Root mean square velocity at `T_(2)` temperature,
`U_(2)=sqrt((3RT_(2))/(M))=sqrt((3R(927+273))/(M))" ...(ii)"`
Eq. (i) divided by Eq. (ii)
`(U_(1))/(U_(2))=sqrt((27+273)/(927+273))=sqrt((300)/(1200))=(1)/(2)`
`U_(2)=2U_(1)`
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