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Assertion : The rms velocity of gas mole...

Assertion : The rms velocity of gas molecules is doubled, when temperature of gas becomes four times.
Reason : `c oo sqrt(T)`

A

If both assertion and reason are true and the reason is correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of assertion.

C

If assertion is true, but the reason is false.

D

If assertion is false but the reason is true

Text Solution

Verified by Experts

The correct Answer is:
A
The rms velocity of gas molecules is given by
`v_(rms)= c = sqrt((3kT)/(m))`
so, `c prop sqrt(T)`
Hence, it is clear that when temperature becomes four times rms velocity will be two times.
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Knowledge Check

  • The rms speed of the perfect gas molecules is doubled if.

    A
    pressure is doubled at constant volume
    B
    pressure is made four times at constant volume
    C
    volume is made four times at constant pressure
    D
    volume is increased by about 42% at constant pressure

  • The root mean square velocity of a gas molecule at any temperature T K of a gas molecule of molecular weight M is

    A
    `sqrt(8RT//M)`
    B
    `sqrt(2RT//M)`
    C
    `sqrt(3RT//M)`
    D
    zero

  • The root mean square velocity of gas molecules is 10km//s . The gas is heated till its pressure becomes four times. The velocity of gas molecules will be

    A
    `10Km//s`
    B
    `20Km//s`
    C
    `40Km//s`
    D
    `80Km//s`