If the electrons gain this energy by collision between hydrogen atoms in a high temperature gas, find the minimum temperature of the heated hydrogen gas. The thermal energy of the heated atoms is given by 3 kB T 2, where the Boltzmann constant is 1.38 x 10-23 J/K. Answer in units of K.
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- A Maxwell-Boltzmann distribution implies that a given molecule (mass m ) will have a speed between 1 and v + dv with probability equal to f(v)dv where ƒ(v) ∞ v² e-mv²/2k³I and the proportionality sign is used because a normalization constant has f(v)dv.) For this distribution, calculate the been omitted. (You can correct for this by dividing any averages you work out by mean speed (v) and the mean inverse speed (1/v). Show that (v)(1/v) = ¼/ .When stars like the Sun die, they lose their outer layers and expose their very hot cores. These exposed cores are called white dwarf stars. A certain white dwarf star has a peak emission wavelength of 0.546 nm. Approximating the star as a blackbody, what is its surface temperature? Wien's Displacement constant is b = 2.898 x 10-3 K m. The Stefan-Boltzmann constant is ? = 5.670 x 10-8 W/m2K4.How does the Boltzmann distribution and statistics explain the behavior of an ideal gas in terms of the distribution of molecular energies and the probability of various energy states?
- 3. The classical partition function of a gas of noninteracting indistinguishable particles is written as exp{- N! 2m Z= where N is the number of particles of mass m, r, and p, are the position and the momentum of the ith particle, B = 1/(kpT), and Tis the temperature of the gas. The volume of the gas is V. (a) Find the analytic expression of the partition function of the gas. (b) Obtain the total mean energy E of the gas from the partition function. (c) Obtain the entropy S of the gas from the partition function and the total mean energy. Lexp(-x³xdx = Va Hint:In kinetic theory of gases, atoms are modeled as point masses m with mean speed v related to temperature T by m v^2 = 3 k T, where k is Boltzmann’s constant. Assuming gas atoms travel several thousand Angstroms between collisions with each other, how cool would hydrogen gas need to be before quantum mechanics would have to be taken into consideration?Experiment 1. The student measures the volume of the gas in the cylinder, places a known mass mon top of the piston, and then increases the temperature of the gas at constant pressure to 273C. Experiment 2. After the gas is allowed to cool back to 0C at 1 atm pressure, the student locks the piston in place, and then increases the temperature of the gas to 273C. Experiment 3. After Experiment 2 is completed, the student unlocks the piston, and a computer-controlled heat source maintains the temperature at a constant 273C. After Experiment 2, how do the pressure and volume change (increase/decrease/remain the same)? After Experiment 3?
- What is the average thermal velocity of a hydrogen molecule H at 27 \deg C? (Assume: Boltzmann constant = 1.38 x 10-23 J/K and the mass of H is m = 3.32 x 10-27 kg)Near the surface of a certain kind of star, approximately one hydrogen atom per 10 million is in the first excited level (n = 2). Assume that the other atoms are in the n = 1 level. Use this information to estimate the temperature there, assuming that Maxwell-Boltzmann statistics are valid.A hydrogen atom ¹H with 200 eV of kinetic energy has a head-on, perfectly elastic collision with a ¹2C atom at rest. Part A Afterward, what is the kinetic energy, in eV, of ¹H? Express your answer in electron volts. KfH = Submit Part B V Kfc = ΑΣΦ Request Answer Afterward, what is the kinetic energy, in eV, of ¹2C? Express your answer in electron volts. ww ΑΣΦ ? ? eV eV