By how many times the absolute temperature of a gas would increase when $u_{r m s}$ of a gas in a container of fixed volume is increased from $5 \times 10^{4} c m s e c^{- 1}$ to $10 \times 10^{4} c m s e c^{- 1}$ ?

Open in App

Solution

Relation between root mean square velocity and temperature
$v_{rms} = \sqrt{\frac{3 R T}{M}}$
So $v_{rms}$ is directtly proportional to $\sqrt{T}$
Thus, $T$ is directly proportional to $(v_{rms})^{2}$
$10 \times 10^{4} / 5 \times 10^{4} = 2$ So V becomes doubled
If v is doubled, T will be four times.

Suggest Corrections

Similar questions

Q. How many times the temperature of a gas would increase, when the

R M S

velocity of the gas molecules in a closed vessel of fixed volume is increased from 5 x 10

^{4}

c m s

^{- 1}

to 10 x 10

^{4}

c m s

^{- 1}

Q. By how many folds the temperature of a gas would increase when the root mean square velocity of the gas molecule in a container of fixed volume from

5 \times 10^{4} c m / s

10 \times 10^{4} c m / s

Q. How much would the root mean square speed become when the absolute temperature of a gas is increased by

16

times ?

The root mean square velocity of an ideal gas in a closed container of fixed volume is increased from $5 \times 10^{4} c m s^{- 1}$ to $10 \times 10^{4} c m s^{- 1}$ Which of the following statement correctly explains how the change is accomplished

Q. In a closed vessel, at a constant volume, URMS of a real gas is increased from

5 \times 10^{4}

cm/s to

10 \times 10^{4}

cm/s. Which statement is true:

Join BYJU'S Learning Program

By how many times the absolute temperature of a gas would increase when urms of a gas in a container of fixed volume is increased from 5×104cmsec−1 to 10×104cmsec−1?

Relation between root mean square velocity and temperature vrms=√3RTMSo vrms is directtly proportional to √T Thus, T is directly proportional to (vrms)2 10×104/5×104=2 So V becomes doubled If v is doubled, T will be four times.

By how many times the absolute temperature of a gas would increase when $u_{r m s}$ of a gas in a container of fixed volume is increased from $5 \times 10^{4} c m s e c^{- 1}$ to $10 \times 10^{4} c m s e c^{- 1}$ ?