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?
When you come out of a river after a dip, you feel cold. Explain.
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.
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
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
One mole of an ideal gas undergoes a process `P = (P_0)/(1+(V/V_0)^2` where `p_0` and `V_0` are constants . Find the temperature of the gas when `V=V_0` .
If the density of oxygen is 1.44 kg/m3 at a pressure of 105 N/m2, find the root mean square velocity of oxygen molecules.
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.
The power radiated by a perfect blackbody depends only on its ______
Compare the rate of radiation of metal bodies at 727 °C and 227 °C.
A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature.
The average translational kinetic energy of gas molecules depends on ____________.
The graph of kinetic energy against the frequency v of incident light is as shown in the figure. The slope of the graph and intercept on X-axis respectively are ______.
Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between P1 and P2?
Explain why there is no atmosphere on moon.
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, KP are related as ______.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
Which of the following materials is diathermanous?
