Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
We know that for a given mass of a gas
`V_(rms) = sqrt((3RT)/M)`
Where R is gas constant
T is the temperature in Kelvin
M is the molar mass of the gas
Clearly, `V_(rms) ∝ sqrt(T)`
As R and M are constants,
`(V_(rms))_1/(V_(rms))_2 = sqrt(T_1/T_2)`
Given, `(V_(rms))_1` = 100 m/s
T1 = 27°C = 27 + 273 = 300 K
T2 = 127°C = 127 + 273 = 400 K
∴ From equation (i)
`100/((V_(rms))_2) = sqrt(300/400) = sqrt(3)/2`
⇒ `(V_(rms))_2 = (2 xx 100)/sqrt(3) = 200/sqrt(3)` m/s
APPEARS IN
संबंधित प्रश्न
When we place a gas cylinder on a van and the van moves, does the kinetic energy of the molecules increase? Does the temperature increase?
It is said that the assumptions of kinetic theory are good for gases having low densities. Suppose a container is so evacuated that only one molecule is left in it. Which of the assumptions of kinetic theory will not be valid for such a situation? Can we assign a temperature to this gas?
A gas is kept in an enclosure. The pressure of the gas is reduced by pumping out some gas. Will the temperature of the gas decrease by Charles's low?
The mean square speed of the molecules of a gas at absolute temperature T is proportional to
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
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg in figure. The vessel itself is kept in a big chamber containing air at atmospheric pressure 100 kPa. The length of the gas column is 20 cm. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the temperature to remain constant throughout the process.
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.
Earth’s mean temperature can be assumed to be 280 K. How will the curve of blackbody radiation look like for this temperature? Find out λmax. In which part of the electromagnetic spectrum, does this value lie? (Take Wien's constant b = 2.897 × 10−3 m K)
The power radiated by a perfect blackbody depends only on its ______
On what, the values of absorption coefficient, reflection coefficient, and transmission coefficient depend, in addition to the material of the object on which the radiation is an incident?
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.
Assuming the expression for the pressure exerted by the gas on the wall of the container, it can be shown that pressure 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 ______.
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.
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.
Explain why there is no atmosphere on moon.
23Ne decays to 23Na by negative beta emission. Mass of 23Ne is 22.994465 amu mass of 23Na is 22.989768 amu. The maximum kinetic energy of emitted electrons neglecting the kinetic energy of recoiling product nucleus is ______ MeV.
If a = 0. 72 and t = 0.04, then the value of r is ______.
At what temperature will therms velocity of a gas be four times its value at STP?
