The molecules of a given mass of gas hav...

The molecules of a given mass of gas have a rms velocity of `200 m//sec` at `27^(@)C` and `1.0 xx 10^(5) N//m^(2)` pressure. When the temperature is `127^(@)C` and pressure is `0.5 xx 10^(5) N//m^(2)` , the rms velocity in `m//sec` will be

`100(sqrt(2))/3`

`100(sqrt(2))`

`400/(sqrt(3))`

None of these

Text Solution

Verified by Experts

The correct Answer is:

Change in pressure will not affect the rms velocity of molecules. So we will calculate only the effect of temperature.
As, `v_(rms) prop sqrt(T)`
`:. (v_(300^@))/(v_(400^@)) = sqrt((300)/(400)) = sqrt((3)/(4)) implies (200)/(v_(400)) = sqrt(3/4)`
`implies v_(400) = (200xx2)/(sqrt(3)) = (400)/(sqrt(3)) m//s`.

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The molecules of a given mass of a gas have rms velocity of 200 m//s at 27^(@)C and 1.0 xx 10^(5) N//m_(2) pressure. When the temperature and pressure of the gas are respectively 127^(@)C and 0.05 xx 10^(5) Nm^(-2) , the rms velocity of its molecules in ms^(-1) is

`(400)/(sqrt(3))`

`(100sqrt(2))/3`

`100/3`

`100 sqrt(2)`

The molecules of a given mass of a gas have r.m.s. velocity of 200 ms^(-1) at 27^@ C and 1.0 x× 10^5 Nm^(-2) pressure. When the temperature and pressure of the gas are respectively, 127^@C and 0.05 x× 10^5 Nm^(-2) , the r.m.s. velocity of its molecules in ms^(-1) is :

`100sqrt2`

`400/(sqrt3)`

`(100sqrt2)/(3)`

`(100)/3`

The molecules of a given mass of gas have an rms velocity of 200 ms(-1) at 27^@C and pressure 1 atm. When the temperature is 127^@C and pressure is 2 atm, the rms velocity in m s^(-1) will be ?

`(100 sqrt(2))/(3)`

`100sqrt(2)`

`(400)/(sqrt3)`