The temperature of the gas is raised from 27$°$C to 927$°$C the root mean square velocity is        

1. $\sqrt{\frac{927}{27}}$ times of the earlier value

2. same as before

3. halved

4. doubled

For 1 mole of gas, the average kinetic energy is given as E. The u_rms of gas is :

1. [2E/M]^1/2

2. [3E/M]^1/2

3. [2E/3M]^1/2

4. [3E/2M]^1/2

The ratio among most probable velocity, mean velocity, and root mean square velocity is given by

1. 1:2:3                           

2. 1: $\sqrt{2}:\sqrt{3}$

3. $\sqrt{2}:\sqrt{3}:\sqrt{\frac{8}{\pi }}$               

4. $\sqrt{2}:\sqrt{\frac{8}{\pi }}:\sqrt{3}$

The numerical value of c_p -c_v is equal to:

1. R             

2. R/M

3. M/R         

4. None of the above

The temperature at which the r.m.s velocity of carbon dioxide becomes the same as that of nitrogen at 21⁰C is-

1. 462 ^oC

2. 273 K

3. 189 ^oC

4. 546 K

The rms velocity of CO₂ at a temperature T (in kelvin) is x cms^–1. At what temperature (in kelvin) the rms velocity of nitrous oxide would be 4x cms^–1

(1) 16 T

(2) 2 T

(3) 4 T

(4) 32 T

The rms velocity of an ideal gas at 27°C is 0.3 ms^–1. Its rms velocity at 927°C (in ms^–1) is [IIT 1996; EAMCET 1991]

(1) 3.0

(2) 2.4

(3) 0.9

(4) 0.6

The rms velocity of hydrogen is $\sqrt{7}$times the rms velocity of nitrogen. If T is the temperature of the gas [IIT 2000]

(1) $T\left(H_2\right)=T\left(N_2\right)$

(2) $T\left(H_2\right)>T\left(N_2\right)$

(3) $T\left(H_2\right)<T\left(N_2\right)$

(4) $T\left(H_2\right)=\sqrt{7}T\left(N_2\right)$

The temperature of an ideal gas is reduced from 927°C to 27°C. The rms velocity of the molecules becomes

(1) Double the initial value

(2) Half of the initial value

(3) Four times the initial value

(4) Ten times the initial value

The ratio,$\frac{ \mathrm{rms} \mathrm{velocity} \mathrm{of} {\mathrm{SO}}_2 }{\mathrm{rms} \mathrm{velocity} \mathrm{of} \mathrm{He}}$, of sulphur dioxide and helium gases at 30ºC is equal to

(A) 4                               

(B) 0.25

(C) 0.10                           

(D) 8