Advertisements
Advertisements
प्रश्न
The mean square speed of the molecules of a gas at absolute temperature T is proportional to
विकल्प
\[\frac{1}{T}\]
\[\sqrt{T}\]
T
T2
Advertisements
उत्तर
T
Root mean squared velocity is given by\[v_{rms} = \sqrt{\frac{3RT}{M}}\]
\[ \Rightarrow \left( v_{rms} \right)^2 = \frac{3RT}{M}\]
\[ \Rightarrow \left( v_{rms} \right)^2 \alpha T\]
APPEARS IN
संबंधित प्रश्न
Comment on the following statement: the temperature of all the molecules in a sample of a gas is the same.
A gas cylinder has walls that can bear a maximum pressure of 1.0 × 106 Pa. It contains a gas at 8.0 × 105 Pa and 300 K. The cylinder is steadily heated. Neglecting any change in the volume, calculate the temperature at which the cylinder will break.
At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth?
Use R = 8.314 JK-1 mol-1
0.040 g of He is kept in a closed container initially at 100.0°C. The container is now heated. Neglecting the expansion of the container, calculate the temperature at which the internal energy is increased by 12 J.
Use R = 8.3 J K-1 mol-1
Figure shows a cylindrical tube of radius 5 cm and length 20 cm. It is closed by a tight-fitting cork. The friction coefficient between the cork and the tube is 0.20. The tube contains an ideal gas at a pressure of 1 atm and a temperature of 300 K. The tube is slowly heated and it is found that the cork pops out when the temperature reaches 600 K. Let dN denote the magnitude of the normal contact force exerted by a small length dlof the cork along the periphery (see the figure). Assuming that the temperature of the gas is uniform at any instant, calculate `(dN)/(dt)`.

The temperature and the dew point in an open room are 20°C and 10°C. If the room temperature drops to 15°C, what will be the new dew point?
At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively).
Answer in brief:
Compare the rms speed of hydrogen molecules at 127°C with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.
Two vessels A and B are filled with the same gas where the volume, temperature, and pressure in vessel A is twice the volume, temperature, and pressure in vessel B. Calculate the ratio of the number of molecules of the gas in vessel A to that in vessel B.
Find the temperature of a blackbody if its spectrum has a peak at (a) λmax = 700 nm (visible), (b) λmax = 3 cm (microwave region) (c) λmax = 3 m (short radio waves). (Take Wien’s constant b = 2.897 × 10-3 m.K).
The number of degrees of freedom, for the vibrational motion of a polyatomic molecule, depends on the ______
Under which condition laws of Boyle, Charles, and Gay-Lussac are valid?
Why the temperature of all bodies remains constant at room temperature?
If the density of nitrogen is 1.25 kg/m3 at a pressure of 105 Pa, find the root mean square velocity of nitrogen molecules.
A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity `omega`. Its kinetic energy is ______.
A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (Figure). If the temperature is increased ______.

Consider a rectangular block of wood moving with a velocity v0 in a gas at temperature T and mass density ρ. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to v0 is A. Show that the drag force on the block is `4ρAv_0 sqrt((KT)/m)`, where m is the mass of the gas molecule.
If a = 0. 72 and t = 0.04, then the value of r is ______.
If a = 0. 72 and r = 0.24, then the value of t is ______.
