Q28 of 31 Page 95

Consider an ideal gas with following distribution of speeds.

(i) Calculate Vrms and hence T ( m = 3.0 X 10-26 kg)


(ii) If all the molecules with speed 1000 m/s escape from the system, calculate new Vrms and hence T.


Root mean square speed of an ideal gas with distribution is given by



Where


=no. of molecules with speed


Let the total no. of molecules be 100


∴




Now, by kinetic theory of gases


Kinetic energy of a molecule is given by






Therefore, vrms and T is 639m/s and 269K respectively


(ii) if all the gas molecules move out of the system, then the remaining molecules =90





Now, by kinetic theory of gases


Kinetic energy of a molecule is given by






Therefore, the rms speed and temperature in this condition is 584m/s and 248K respectively


More from this chapter

All 31 →
26

An insulated container containing monoatomic gas of molar mass m is moving with a velocity vo. If the container is suddenly stopped, find the change in temperature.

 27

Explain why

(a) there is no atmosphere on moon.


(b) there is fall in temperature with altitude.


 29

Ten small planes are flying at a speed of 150 km/h in total darkness in an air space that is 20 × 20 × 1.5 km3 in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius 10m.

 30

A box of 1.00m3 is filled with nitrogen at 1.50 atm at 300K. The box has a hole of an area 0.010 mm2. How much time is required for the pressure to reduce by 0.10 atm, if the pressure outside is 1 atm.