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The probability of finding an N2 molecule at ambient temperature at 515 m/s is zero.
True or False?
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- Determine how many times per second each molecule moving with rms speed would move back and forth across a 6.6 mm-long room on average, assuming it made very few collisions with other molecules.To find Vx use the equation v^2=v^2x+v^2y+v^2zand the fact that molecules have no preferred direction.a) Calculate the mean free path in meters of a nitrogen molecule (with a mass m=4.68×10¬26 kg) located in Earth's atmosphere at sea level. Assume a temperature of T=300 K and a number density of particles of 1019 cm-3. b) Assuming that the collision cross-section of the molecule is o = 2x10-10 frequency v in Hertz and the time between collisions t in seconds. m, compute the collisionUnder the Equipartition Principle, in the high temperature limit, molecular heat capacity should be 1 -NR, where N is the number of atoms in 2 the molecule and R is the gas constant. O True O False
- The speed of a molecule in a uniform gas at equilibrium is a random variable V whose density function is given by S(0) = av²e-b*; D > 0, where b = m/(2kT) and k, T and m denote Boltzmann's constant, the absolute temperature, and the mass of the molecule, respectively. (a) Derive the distribution of W = mV² /2, the kinetic energy of the molecule. (b) Find E (W).Calculate rms velocity of CO2 molecule at NTP.The 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.
- Determine how many times per second each molecule moving with rms speed would move back and forth across a 6.4 mm -long room on the average, assuming it made very few collisions with other molecules.To find vx use the equation v2=v2x+v2y+v2z and the fact that molecules have no preferred direction. vrms= 473 m/sRoom temperature is 20 °C. Calculate the ratio v₂/V1, where v₁ = the rms speed of a nitrogen molecule (mass = 30 u) and v₂ = the speed of a helium atom (mass = 4 u), in the room. V1 OA: 2.74 OB: 3.64 OC: 4.84 OD: 6.44 OE: 8.57 OF: 11.40 OG: 15.16 OH: 20.16Estimate the mean free path of a nitrogen molecule in a cylinder nitrogen at 2 atm and a temperature of 17 oC. Take the radius to be roughly equal to 1 x10-10 m. Boltzmann constant 1.38 x10-23 J/K.
- For one mole of Van der Waals gas, find Pc, Vc, and Tc from the condition T, dP / dV = 0 d'P / dV 2= 0 at constant temperature. Find the Pc Vc/ RTc ratio.Suppose you are in a room that is at a temperature of 293.02K. What is the approximate RMS velocity of an O2 molecule in this room (in units of meters per second)?Figure shows a hypothetical speed distribution for a sample of N gas molecules. Find probability of a molecule(a) to lie in between 0 →Vo(b) to lie in between Vo→ 2 Vo(c) to lie in between 0→ 2 Vo(d) What fraction of molecules have speed in between 0.5 to lie in between 0.5 Vo→1.5 Vo