Advertisements
Advertisements
Question
Two molecules of a gas have speeds of 9 × 10 6 ms−1 and 1 × 106 ms−1, respectively. What is the root mean square speed of these molecules?
Advertisements
Solution
For n-molecules, we know that
`v_(rms) = sqrt((v_1^2 + v_2^2 + v_3^2 + ...... + v_n^2)/n` .....`[(v_(rms) = "root mean"),("square velocity")]`
Where v1, v2, v3 ....... vn are individual velocities of n-molecules of the gas.
For two molecules,
`v_(rms) = sqrt((v_1^2 + v_2^2)/2` ......[v1, v2, v3 ....... vn are individual velocity]
Given, `v_1 = 9 xx 10^6` m/s
And `v_2 = 1 xx 10^6` m/s
∴ `v_(rms) = sqrt(((9 xx 10^6)^2 + (1 xx 10^6)^2)/2`
= `sqrt((81 xx 10^12 + 1 xx 10^12)/2`
= `sqrt(((81 + 1) xx 10^12)/2`
= `sqrt((82 xx 10^12)/2`
= `sqrt(41) xx 10^6` m/s
APPEARS IN
RELATED QUESTIONS
Do you expect the gas in a cooking gas cylinder to obey the ideal gas equation?
Consider a gas of neutrons. Do you expect it to behave much better as an ideal gas as compared to hydrogen gas at the same pressure and temperature?
If the molecules were not allowed to collide among themselves, would you expect more evaporation or less evaporation?
The process on an ideal gas, shown in figure, is
During an experiment, an ideal gas is found to obey an additional law pV2 = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.
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 weather report reads, "Temperature 20°C : Relative humidity 100%". What is the dew point?
The condition of air in a closed room is described as follows. Temperature = 25°C, relative humidity = 60%, pressure = 104 kPa. If all the water vapour is removed from the room without changing the temperature, what will be the new pressure? The saturation vapour pressure at 25°C − 3.2 kPa.
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).
Calculate the energy radiated in one minute by a blackbody of surface area 200 cm2 at 127 °C (σ = 5.7 x 10-8 J m-2 s-1 K-4)
What is the microscopic origin of temperature?
Explain in detail the kinetic interpretation of temperature.
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 ______.
An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be ______.
The molecules of a given mass of a gas have root mean square speeds of 100 ms−1 at 27°C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?
A gas mixture consists of molecules of types A, B and C with masses mA > mB > mC. Rank the three types of molecules in decreasing order of rms speeds.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
At what temperature will therms velocity of a gas be four times its value at STP?
If a = 0. 72 and r = 0.24, then the value of t is ______.
2000 calories of radiant heat is incident on a body. If the body absorbs 550 calories of heat, find the coefficient of emmission of the body.
