State down the integral you would need to evaluate

Reference no: EM13184463

The following questions pertain to the magnitude of the x-component of the speed(absolute value of the velocity) cx=|vx| of atoms in a gas, whose probability distriubution has the form P(cx)= ae^-bc2/x.

A. Write down the integral you would need to evaluate in order to calculate the avg value of c^2/x.

B. Evaluate the above integral in terms of the constants a and b.

C. Express b in terms of the mass m of each atom and the temperature T of the gas( and other constants), given that the Boltsmann factor in P(cx) pertains to the x- component of the kinetic energy of each atom in the gas.

D. How should the value of a differ from that in Eq - P(vx)dvx= sq root. m/2pikbT e^-mv2/x/2kbT dvx given that speed cx includes both the corresponding positive and negative velocities, and so the probability of observing a speed cx is twice that of observing the corresponding velocity vx?

E. Use the above results to express the avg value of c2/x in terms of m and kbT, and then show that the avg kinetic energy in the x-direction <ex>=1/2m<c2/x> has the expected value.

Reference no: EM13184463

Questions Cloud

Compute the radius of an iridium atom : Calculate the radius of an iridium atom, given that Ir has an FCC crystal structure, a density of 22.4 g/cm3,

Demonstrated its social and environmental accountability : Discuss the way in which BHP Billiton has demonstrated its social and environmental accountability and discuss the stance and initiatives of the Australian accounting profession on corporate social responsibility

Compute the van''t hoff factor : Calculate the van't Hoff factor (i) for this solution. 2. Calculate the vapor pressure at 25 ?C of an aqueous solution that is 5.80% NaCl by mass.

Indicate the desirability of discounting the price : You are the manager of a large automobile dealership who wants to learn more about the effectiveness of various discounts offered to customers over the past 14 months. Following are the average negotiated prices for each month and quantities sold ..

State down the integral you would need to evaluate : The following questions pertain to the magnitude of the x-component of the speed(absolute value of the velocity) cx=|vx| of atoms in a gas, whose probability distriubution has the form P(cx)= ae^-bc2/x. A. Write down the integral you would need to ..

Compute the beginning balance in the cash account : Compute the beginning balance in the cash account and how much cash was provided by (or used in) operating activities?

Describe the u.s. market for wine under free trade : Assuming that American imports of wine are a small part of total world wine production, draw a graph for the U.S. market for wine under free trade. b.) Now suppose that a tariff is place on the importation of wine into the United States to protec..

Explain what is the hamiltonian of the particle : Consider a particle that is confined by a one-dimensional quadratic (harmonic) potential of the form U9x)=Ax^2 (where A is a positive real number). A. What is the Hamiltonian of the particle(expressed as a function of velocity v and x)?

Define a molecule will have a velocity : Predict the probability P9v) that a molecule will have a given total velocity of more specifically P(v)dv is the probability that a molecule will have a velocity btwn v and v+dv.

User Account

All Pages