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The mean free path in a sample of gas is 30 nm. The collision feequency is 3 x 109 s-1.
Calculate the mean relative speed in m s-1.
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- If all the gas particles are in a state of moving toward each other and causing a collision, then the calculated velocity is... A. The most possible speedB. Average speedC. Mean square root velocityD. Relative speedE. Speed squaredThe mean free path λ and the mean collision time T of molecules of a diatomic gas with molecular mass 6.00 x10^-25 kg and radius r=1.0x10^-10m are measured.From these microscopic data we can obtain macroscopic properties such as temperature T and pressure P? If yes, consider λ=4.32x10^-8m and T=3.00x10^-10s and calculate T and P.a)It's not possible.b)Yes,T=150K and P~2.04atm.c)Yes,T=150K and P~4.08atm.d)Yes,T=300K and P~4.08atm.e)Yes,T=300K and P~5.32atmf)Yes,T=400K and P~4.08atmg)Yes,T=400K and P~5.32atm.A)An ideal gas is confined to a container at a temperature of 330 K.What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.) B)2.00 mol of the helium is confined to a 2.00-L container at a pressure of 11.0 atm. The atomic mass of helium is 4.00 u, and the conversion between u and kg is 1 u = 1.661 ××10−27 kg.Calculate vrmsvrms. (Express your answer to three significant figures.) C)A gold (coefficient of linear expansion α=14×10−6K−1α=14×10−6K−1 ) pin is exactly 4.00 cm long when its temperature is 180∘∘C. Find the decrease in long of the pin when it cools to 28.0∘∘C? (Express your answer to two significant figures.)
- You measure the average free path λ and the average collision time τ of the molecules of a diatomic gas of molecular mass 6.00 × 10-²⁵ kg and radius r = 1.0 x 10-¹⁰ m. From these microscopic data can we obtain macroscopic properties such as temperature T and pressure P? If so, consider λ = 4.32 x 10-⁸ m and τ = 3.00 x 10-¹⁰ s and calculate T and P. indicate the correct answer: 1- Not possible2- Yes, T =150 K and P ~ 2.04 atm.3- Yes, T = 150 K and P ~ 4.08 atm.4- Yes, T = 300 K and P ~ 4.08 atm.5- Yes, T = 300 K and P ~ 5.32 atm6- Yes, T = 400 K and P ~ 4.08 atm.7- Yes, T = 400 K and P ~ 5.32 atm. obs.: If necessary, consider: R = 8.314 J/mol∙K1 cal = 4.19 Jkb =1,38 x 10⁻²³ m² kg s⁻² K⁻¹A frictionless piston of mass m = 3.0 kg is a precise fit in the narrow vertical cylindrical neck of a large container of volume V = 1000 litres and can move frictionless. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A = 1.00 x 10-4 m2. a) Assuming that the pressure and volume of the gas change slowly and isothermally, determine the differential equation of motion for small displacements of the piston about its equilibrium position and hence calculate the angular frequency of oscillation. [Hint: find an equilibrium pressure and consider how small displacement of the piston from the equilibrium position changes the volume and pressure in the vessel]. b) Without calculation, consider whether the frequency will increase or decrease if the pressure and volume of the gas were to change adiabatically. Explain your reasoning.Initially, the translational rms speed of a molecule if an ideal gas is 560 m/s. The pressure and volume of this gas are kept constant, while the number of molecules is increased by a factor of 7. What is the final translational rms speed of the molecules?
- Hydrogen gas is cooled to 100 K, while the pressure is reduced to 0.1 Pa. a) Determine the mean free path A and the average frequency of collision. b) What are the rms speed and the average kinetic energy of a molecule? c) What is the momentum flux of the gas on the container? d) What are the most probable free path, the most probable speed, and the most probable velocity?In interstellar space it is estimated that atomic hydrogen exists at a concentration of one particle per cubic meter. If the collision diameter is 2.5 x 1010 m, calculate the mean free path 2. The temperature of interstellar space is 2.7 K. 2.What is the rms speed of nitrogen molecules contained in an 8.5m3 volume at 2.9 atm if the total amount is 2100 mol? What will be rms speed of oxygen in same condition? 2.
- In a period of 9.00 s, 5.00 × 1023 nitrogen molecules strike a wall of area 5.80 cm². Assume the molecules move with a speed of 340 m/s and strike the wall head-on in elastic collisions. What is the -26 kg. pressure exerted on the wall? Note: The mass of one N, molecule is 4.65 x 10 3.513 Calculate the momentum change in each second and use the impulse-momentum theorem to relate the momentum change to the average force between the wall and the nitrogen in order to find the pressure. kPa Need Help? Read It Master ItThe mean free path for a certain gas is 2.03×10−7 m. and the radius of an atom of said gas is approximately 1.19×10−11 m. What is the density of the gas in moles per cubic meter under these conditions?prove average total kinetic energy = 2kT for gas molecules crossing a spherical area, with the following equations.