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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 what temperature, pressure remaining unchanged, will the rms velocity of hydrogen be double its value at NTP ?

A

819 K

B

`819^(@)C`

C

1000 K

D

`1000^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
B
As, `C^(2) prop T :. (C)/(C_0) = sqrt((T)/(T_0))`
As, `C = 2 C_(0) :. Sqrt((T)/(T_0)) = sqrt((273+t)/(273+0)) = 2`
or, `273 + t = 4 xx 273 = 1092`
`t = 1092 - 273 = 819^(@)C`.
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