Using the result fx²¹e-αx² dx = VRMS = 3RT M 3 8a² Va derive from the Maxwell-Boltzmann distribution the expression for the RMS speed:
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- High-intensity focused ultrasound (HIFU) is one treatment for certain types of cancer. During the procedure, a narrow beam of high-intensity ultrasound is focused on the tumor, raising its temperature to nearly 90°C and killing it. A range of frequencies and intensities can be used, but in one treatment a beam of frequency 4.40 MHz produced an intensity of 1425.0 W/cm. The energy was delivered in short pulses for a total time of 3.40 s over an area measuring 1.80 mm by 5.40 mm. The speed of sound in the soft tissue was 1580 m/s, and the density of that tissue was 1509.0 kg/m?. What was the wavelength A of the ultrasound beam? = m How much energy Eotal Was delivered to the tissue during the 3.40 s treatment? J Etotal = terms of use contact us help about us privacy polícy careers Show All V VS T.jpeg Free-Fall-Phet.docx free fall.png V VS T.jpeg FII F10 F8 F7 000 * F5 F6 aロImagine a photon gas at an initial temperature of T = 1.4 K. What is the temperature of the photon gas (in K) after it has undergone a reversible adiabatic expansion to 2 times its original volume?In this problem you will consider the balance of thermal energy radiated and absorbed by a person. Assume that the person is wearing only a skimpy bathing suit of negligible area. As a rough approximation, the area of a human body may be considered to be that of the sides of a cylinder length L = 2.0 m and circumference C = 0.8 m. For the Stefan-Boltzmann constant use o = 5.67 x 10-8 W/m2 /K4.
- Consider a system with 1000 particles that can only have two energies, ɛ, and with ɛ, > E,. The difference between these two values is Aɛ = ɛ, -& . Assume that gi = g2 = 1. Using the %3D %3D equation for the Boltzmann distribution graph the number of particles, ni and m, in states & n2, E and E, as a function of temperature for a Aɛ = 1×10-2' J and for a temperature range from 2 to 300 K. (Note: kg = 1.380x10-23 J K-!. %3D %3D (s,-s,) gLe Aɛ/ n2 or = e n,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 fuel-efficient car is able to convert the chemical potential energy of gasoline into translational kinetic energy at an efficiency of 78.4%. If there is 8742 kJ of chemical potential energy in one tank of gas, what is the amount of translational kinetic energy produced. How to manipulate formula eff=output/input x 100
- For a system of particles at room temperature, how large must € - μ be before the Fermi-Dirac, Bose-Einstein, and Boltzmann distributions agree within 1% ? Is this condition ever violated for the gases in our atmosphere? Explain.how do I calculate an average energy when there are three psi unknowns? PSI= c1*psi1(x) + c2*psi2(x) + c3*psi3(x) also, how do I calculate probability when there is an energy given?Using the same procedure to determine the fundamental equation of chemical thermodynamics (dG = –SdT + VdP) from the Gibbs free energy of a system (G = H – TS), can you please explain how to find the analogous fundamental equation for (A=U-TS)? Also, can you please handwrite the formula down instead of typing? I get confused with typed formulas sometime.
- For a gas of nitrogen (N2) at room temperature (293 K) and 1 atmosphere pressure, calculate the Maxwell-Boltzmann constant A and thereby show that Bose-Einstein statistics can be replaced by Maxwell-Boltzmann statistics in this case.The Earth reradiates the energy it receives from the Sun as a black body. We can calculate the effective temperature of the Earth using the Stefan-Boltzmann equation F = sT4 where we solve for the Temperature T. We use for the energy flux the amount of energy absorbed per second Le divided by the Earth's surface area from which the energy is radiated 4pd2 so that the flux is = Le/(4pd2). Here d is the radius of the Earth given above and s is the Stefan-Boltzmann constant. And the effective temperature is:Te4 = (Le/(4pd2))/s = Le/(4spd2) = __________________ K4and taking the square root of Te4 twice in succession we get the effective Temperature Te:Te = [Le/(4spd2)]0.25 = _________________ Kfor the temperature of the effective Earth. What is the temperature in the Celsius scale? __________ C. (Do I need to tell you how to convert from Kelvin to Celsius? If you don't know look it up in your textbook!!)Problem 2) Consider the following Maxwell Boltzmann distribution of molecular speeds: P(v) = 4( m 27kBT. mp² v²e 2kgT To calculate average values for say f(v) (function of v) one just integrates f(v) with P(v)dv from zero to infinity = P(v)f(v)dv, where signifies average of f(v). Of course, the distribution should be normalized: P(v)dv=1, (is a requirement for any probability distribution). a) Check the last equation. b) Calculate the average of v. c) Calculate the average of v². d) Calculate from c) the RMS value of the speed. e) Calculate the most probable value of v. f) Square the results of b, d and e and rank them from smallest to the largest value.