Find the temperature distribution T(r,θ,z) inside a cylinder of height z= 20 and radius r= 8 , if the cylinder temperature is zero in all surface except the bottom circular surface where it is divided two halves , the first is held at T1= 100 c and the other is held at T2=200 c.

please use laplace equation and show me the solution with the details of the derivation .

How can I conduct an home experiment to explore:

How thick is the liquid water film beneath a sliding ice cube?

why does the wiedemann franz law always work at high temperatures? why are the scattering processes simular at that range, and what would happen if a electric field is applied

how does the linearized boltzmann equation affect transport properties

give the equation for current density in form of fermi dirac distribution function and graph it

1.carry out the dimensional analysis of a simple pendulum
2.The dimensional analysis of walking
3.Dimensional analysis of a solid sphere moving through a fluid

(4) Consider a system described by the Hamiltonian H, H = 0 a a 0 !,
where a is a constant. (a) At t = 0, we measure the energy of the system, what possible values will we obtain? (b) At later time t, we measure the energy again, how is it related to its value we obtain at t = 0 ? (c) If at t = 0, the system is equally likely to be in its two possible states, write down the most general state of the system at t = 0. (d) What is the probability that at time t = 5, the system will be in a state different from its initial state?. (e) Suppose the above Hamiltonian describes a spin-1/2 particle in a magnetic field. If Sx is found to be ¯h/2, what is the probability of getting Sz equal to ¯h/2?. What is the probability of getting Sy equal to −¯h/2 ? What is the probability of getting Sx equal to −¯h/2
2

Indicate whether the following statements are always true or can be false.
True False  If an object's speed does not change, no net force is acting on the object.
True False  If two objects are under the influence of equal forces, they have the same acceleration.
True False  The net force which acts on an object which maintains a constant velocity is zero.
True False  An object's velocity will change if a net force acts on the object.
True False  A truck initially moving at a constant velocity will slow down unless a small net force is applied.
True False  During the collision of a car with a large truck, the car exerts a lesser force on the truck than the truck exerts on the car.

Solid-state physics, Band gap

a, How does the size of the band gap depend on the strength of the periodic potential?

b, Which type of material would you expect to have the stronger periodic potential, a metal or an insulator? Why?

Please explain thoroughly

A metal surface is susceptible to a photoelectric threshold frequency of 8.529*10>14Hz. Will the monochromatic UV light sources of wavelengths 283 nm, 342 nm, and 363 nm be able to eject photoelectrons from the metal. If so what is the speed of the fastest electron ejected?

An electron in a TV camera tube is moving at 7.20×10⁶ m/s in a magnetic field of strength 59 mT. Without knowing the direction of the field, what can you say about the greatest and least magnitude of the force acting on the electron due to the field? Maximum force?

Minimum force?

At one point the acceleration of the electron is 6.327×10¹⁶ m/s². What is the angle between the electron velocity and the magnetic field? (deg)

Solid-state physics

a, How many electrons are needed to fill all states in a band?

b, What is the meaning of the Fermi energy?

c, What is the Fermi surface of a metal?

Please explain thoroughly

Chemical reactions are often described using a three state model:

Reactants→Transition State→ProductsReactants→Transition State→Products

In most cases the energy of the transition state is much higher than the energy of the reactant state. This means that the reaction cannot proceed until there is a random thermal fluctuation large enough to `kick' the reactant molecule(s) up to the transition state energy. Say we have a reaction in which the transition state is 9.0×10⁻²⁰ J above the reactant state.

a.) Calculate the ratio of the probability the system is in the transition state to the probability that it is in the reactant state (P_TS/P_R) at 37 C.

P_TS/P_R = (7.3 x 10^-10 is correct)

b.) Use your answer above to estimate the time it takes for the reaction to occur spontaneously at 37 C. Assume that the system samples a new microstate every nanosecond (10⁻⁹ s).

[Hint: If you throw a 6-sided die, what is the probability you will get a 3? How many times would you expect to have to throw the die to get a 3? Using similar logic, use your answer in the first part to tell you how many times the system has to try before it gets a fluctuation that is big enough.]

time: (2.1 x 10^-8 s is incorrect)

c.) One way to speed up the reaction is to heat the system. If the temperature is increased to 1000 K, how long does it take for the reaction to occur?

time: (.009325 s is incorrect)

d.) In biological systems it is not feasible to accelerate reactions by heating them to 1000 K. Instead, the reactions rely on enzymes that catalyze reactions by lowering the energy of the transition state. If catalyzed reaction has a transition state energy 2.0×10⁻²⁰ J, what is the approximate reaction time? Use a temperature 37 C.

time: (6.52 x 10^-9 s is incorrect)

e.) Finally, estimate the uncatalyzed reaction time if the transition state is not a unique microstate, but actually an ensemble of 100 microstates. Use a temperature 37 C.

time: (4.675 x 10^-9 s is incorrect)

derive the Jarzynski equality from the Crooks fluctuation theorem (CFT) and the non-equilibrium partition identity.

A particle of mass M moves along a straight line with initial speed vi. A force of magnitude Fpushes the particle a distance D along the direction of its motion.

A) Find vf, the final speed of the particle after it has traveled a distance D. Express the final speed in terms of vi, M, F, and D.

B) By what multiplicative factor RK does the initial kinetic energy increase, and by what multiplicative factor RW does the work done by the force increase (with respect to the case when the particle had a mass M)? If one of the quantities doubles, for instance, it would increase by a factor of 2. If a quantity stays the same, then the multiplicative factor would be 1. You should enter the two factors separated by a comma.

C) By what factor RK does the initial kinetic energy increase (with respect to the first situation, with mass M and speed vi), and by what factor RW does the work done by the force increase?