Derive the expression for the most probable speed. You have to find the maximum of the...
Use Maxwell's speed distribution law to derive the expression for the most probable speed of molecules in a sample of gas dN/N = 4/squareroot pi [M/2RT]^3/2 v^2 e^-Mv^2/2 RT dv
4. Derive the expression for the rms velocity using the Maxwell-Boltzmann distribution. *Please show steps, formulas, descriptions.
Derive an expression for total revenue. Find its critical value. Is it a min or max? Explain how you know. 4. Suppose you have the following demand curve: Pa = a - bQ Derive an expression for total revenue. Find its critical value. Is this a minimum or maximum? How do you know? Explain/Show work.
(20 pts) Derive the expression for the necessary magnetic flux ( function of am, for as a operation of a DC motor in the constant power region. Recall that you can find the maximum power of the motor at the base speed. Your expression for ø should only be in terms of am, the base speed ob, and the maximum magnetic flux dmax. Note that the maximum torque is not a necessary parameter for determining the needed expression (20 pts)...
3. Derive the following relationship between the Helmholtz free energy F and the partition function Z for a system of N particles: (a) Starting with the thermodynamic definition F-U-TS, substitute the statistical mechanics results which give U and S in terms of occupation numbers n, state energies e and the most probable number of microstates t* to find, (b) Write out texplicitly in terms of occupation numbers using Stirling's approxima- tion (check the Lagrange multiplier derivation of the Boltzmann distribution)...
Please leave a step by step guide on how to do this please? Thank you so much a) Derive an expression for the value ofl corresponding to the most highly populated rotational energy level of a spherical rotator(Umax). For spherical rotator each energy level is (2) +1)2 - fold degenerate and energy is given by E-hcBJ1). The population N, of molecules in energy level J is given by the Boltzmann expression gje where N is the total number of molecules...
Hydrogen atoms have 2 main isotopes: 1H and 2H. With these sketch the Maxwell-Boltzmann speed distribution for each isotope.Make sure to include data at v=0 and as v infinity. Make sure shape of curve is precise
Using the function of molecular speed distribution Maxwell - Boltzmann for an ideal gas mono-atomic, given by: and the formula for the gaussiano integral and its n momentums are given by: Find an expresion in terms of m, T, N and k, for: the average molecular speed, the average speed square, the deviation "standard", the average molecular kinetic energy, and the pressure exerted by the gas.
3. Consider a vessel of nitrogen gas in equilibrium with the surroundings at 300 K. Assume ideal gas behavior. (a) If you were to measure the speed of a nitrogen molecule, what speed are you most likely to find? (b) How fast does a nitrogen molecule need to be traveling to be among the top 1%? (Hint: Use the Maxwell-Boltzmann distribution.)