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The pressure exerted by an ideal gas is ...

The pressure exerted by an ideal gas is `P = (1)/(3) (M)/(V)C^(2)`, where the symbols have their usual meaning. Using standard gas equation, PV = RT, we find that `C^(2) = (3 RT)/(M) or C^(2) oo T`. Average kinetic energy of translation of one mole of gas ` =(1)/(2) MC^(2) = (3 RT)/(2)` with the help of the passage given above, choose the most appropriate alternative for each of the following quetions :
At waht temperature, pressure remaining unchanged, will the rms velocity of a gas be half its value at `0^(@)C`?

A

204.75 K

B

`204.75^(@)C`

C

`-204.75 K`

D

`-204.75^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
D
If `C = 1/2 C_(0)then sqrt((T)/(T_0)) = 1/2 `
`sqrt((273+t)/(273+0)) = 1/2 or (273+t)/(273) = 1/4`
`t = 273/4 - 273 = 68.25 - 273 = -204.75^(@)C`.
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