Advertisements
Advertisements
प्रश्न
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).
Advertisements
उत्तर
Given: Standard Temperature Pressure (S.T.P) i.e. T2 = 273 K, M01 (oxygen) = 32 × 10-3 kg/mol, M02 (helium) = 4 × 10-3 kg/mol,
`"v"_"rms" = sqrt("3RT"/"M"_0)`
The rms speed of oxygen molecules, `"v"_1 = sqrt("3RT"_1/"M"_01)` and that of helium molecules,
`"v"_2 = sqrt("3RT"_2/"M"_02)`
when v1 = v2 ,
`sqrt("3RT"_1/"M"_01) = sqrt("3RT"_2/"M"_02)`
`∴ "T"_1/"M"_01 = "T"_2/"M"_02`
∴ Temperature, T1 = `"M"_01/"M"_02. "T"_2`
`= ((32 xx 10^-3)(273))/(4 xx 10^-3)`
= 2184 K
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?
Comment on the following statement: the temperature of all the molecules in a sample of a gas is the same.
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?
Is it possible to boil water at room temperature, say 30°C? If we touch a flask containing water boiling at this temperature, will it be hot?
The pressure of an ideal gas is written as \[P = \frac{2E}{3V}\] . Here E refers to
The mean square speed of the molecules of a gas at absolute temperature T is proportional to
Which of the following quantities is the same for all ideal gases at the same temperature?
(a) The kinetic energy of 1 mole
(b) The kinetic energy of 1 g
(c) The number of molecules in 1 mole
(d) The number of molecules in 1 g
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.
The temperature and pressure at Simla are 15.0°C and 72.0 cm of mercury and at Kalka these are 35.0°C and 76.0 cm of mercury. Find the ratio of air density at Kalka to the air density at Simla.
Use R=8.314J K-1 mol-1
Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is 0.002 m3. One of the tubes gets punctured and the volume of the tube reduces to 0.0005 m3. How many moles of air have leaked out? Assume that the temperature remains constant at 300 K and that the air behaves as an ideal gas.
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` .
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.
The weather report reads, "Temperature 20°C : Relative humidity 100%". What is the dew point?
If a = 0.72 and r = 0.24, then the value of tr is ______.
In an ideal gas, the molecules possess ______.
The emissive power of a sphere of area 0.02 m2 is 0.5 kcal s-1m-2. What is the amount of heat radiated by the spherical surface in 20 seconds?
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 power radiated by a perfect blackbody depends only on its ______
Calculate the value of λmax for radiation from a body having a surface temperature of 3000 K. (b = 2.897 x 10-3 m K)
Why the temperature of all bodies remains constant at room temperature?
The average translational kinetic energy of a molecule in a gas becomes equal to 0.49 eV at a temperature about (Boltzmann constant = 1.38 x 10-23 JK-1) ____________.
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.
A proton, a deuteron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is ______.
Two gases A and B are at absolute temperatures of 360 K and 420 K, respectively. The ratio of the average kinetic energy of the molecules of gas B to that of gas A is ______.
When the temperature of an ideal gas is increased from 27°C to 227°C, its speed is changed from 400 ms-1 to vs, and Then vs is ______.
Assuming the expression for the pressure P exerted by an ideal gas, prove that the kinetic energy per unit volume of the gas is `3/2` P.
Show that the average energy per molecule is directly proportional to the absolute temperature ‘T’ of the gas.
