Considering a gas consisting of only a single kind of molecule, derive the relation between collision time and scattering cross section.
Considering a gas consisting of only a single kind of molecule, derive the relation between collision...
Definition of cross section We use the scattering angle to define the cross section weak scattering strong scattering θ (scattering angle) Relation between scattering angle and cross section Number of particles scattered into the solid angle d2 (6,9) is given by dN-N σ (θ, φ) dS: N do (θ, φ) → σ (0、4) represents the occurrence rate of a scattering process with θ、φ This number is equal to the number of particles passing through the area db b dp, given...
Derive a relation between the diffusion coefficient (D) and pressure and temperature for an ideal gas. Using this relation, calculate the percentage of change in D for a given ideal gas if temperature is increased by 40% in a constant-volume process.
(a) Show that for a gas, the mean free path between collisions is related to the mean distance between nearest neighbors r by the approximate relation 1 r(r2/0) where o is the collision cross- section. (b) Given that the molecular radius of a gas molecule such as O2, N2, or CO2 is about 0.15 nm, estimate the value of r and for air at STP (standard temperature and pressure, T = 273 K, p = 1.00 atm = 1.01 X...
2. (20 points) Derive a) the relation between hydrostatic pressure gradient and specific gravity considering the force balance with respect to an infinitesimal volume submerged in a fluid, and b) prove that there is no pressure variation normal to the direction of gravitational acceleration
4. Starting from the first law of thermodynamics and the ideal gas law, derive the relation between T2/T1 and P2/P1, in a isentropic compression, where subscripts 1 and 2 indicate the start and end of the process.
A single gas molecule of inertia m is trapped in a box and travels back and forth with constant speedv between opposite walls A and B a distance lapart. At each collision with a wall, the molecule reverses direction without changing speed. 1) Write algebraic expressions for the magnitude of the change in momentum of the molecule as it collides with wall B. Express your answer in terms of some or all of the variables m, v, and l. delta(p)=??...
By considering the volume V and entropy S as the two independent variables in the thermodynamic equation dE = TdS−PdV , derive the Maxwell relation between the derivatives ∂T/ ∂V and ∂P/ ∂S .
2. In addition, we will derive an expression for the pressure that a gas exerts on the walls of a container. The remainder of this pre-lab asks you to take the first steps in that process: Imagine that the gas inside a cube of side length L has such low density that its particles almost never collide with each other; they collide only with the walls of the container. Assume a model of the gas as tiny moving billiard balls...
only answer: what is the relation between the original and the mirror? and why 2. (6 points) 1,3-Dichloro-1,2-propadiene is shown below. Draw the mirror image of this molecule. Is the mirror image superimposable on the original molecule? What is the relationship between the two drawings of 1,3-dichloro-1,2-propadiene? Explain. Note: no credit will be given for answers without explanations.
1) When considering single molecule vs ensemble kinetics for a simple dissociation reaction such as release of product from an enzyme (E:P <-> E + P), at the single molecule level is the product released at the rate of the rate constant or is it released very rapidly but the lifetime of the E:P state varies from molecule to molecule? 2) What or where in a cell are you likely to find only one-to-two molecules of a substrate? 3) For...