Q: Problem 1: Maxwell relations a) Functions encountered in physics are generally well enough behaved…
A:
Q: There is no Bose-Einstein condensation at nonzero temperatures in a non-interacting Bose gas in two…
A: Non-interacting Bose gas is the starting point for our discussions. Its propertiesare determined by…
Q: Consider a system of two Einstein solids, where the first "solid" contains just a single oscillator,…
A: The expression for the micro states for first Einstein solid is, Here, N is the number of harmonic…
Q: A smooth flat plate with length L and width b is immersed in a stream of fluid (and ) flowing at U.…
A: Given data: The length of the smooth flat plate is L The width of the smooth flat plate is b The…
Q: 3kg of partick is exercistng sīnusoidally in one-dinension The displacement B X= (Sm)cos( mand /s)t-…
A:
Q: Calculate the change in Gibbs and Helmholtz free energies for one mole of an ideal gas that…
A: As, the temperature is constant, change in P will eventually results in change in V. Now, we know…
Q: State the Borel-Cantelli Lemma for independent sequences of events
A: Introduction: An independent event is an event that has no connection to another event's chances of…
Q: 1-49. Maximize N! W(N1, N2,..., NM) = IN,! with respect to each N, under the constraints that EN,=N…
A:
Q: The stationary States be when the potential energy of the particle does not depend on * .the…
A: Introduction: The stationary state is called a stationary state because it remains in the same…
Q: for maxwell distribuition Preve tat. sx(는)- 4. TT
A: The Maxwell's velocity distribution is given by, f(v)=m2πkT3e-mv22kT (1) The average velocity is…
Q: A single-variable differential equation without time delay cannot oscillate. (Hint. What would a…
A: Introduction: Delay differential equations are a type of differential equation in which the…
Q: 2051 Ideal monatomic gas is enclosed in cylinder of radius a and length L The cylinder rotates with…
A: To answer: (a) What is the Hamiltonian in the rotating coordinates system? (b) What is the partition…
Q: Use the mapping function w = z2 to find the streamlines for the flow of wateraround the inside of a…
A: Consider the mapping function, w=z2 Differentiate with respect to z. dwdz=2z =0 When the real…
Q: random walk.
A: We have a random walk problem.
Q: Q Calculate the velocity of longitudinal and shear elastic waves in a cubical crystal along (111)…
A:
Q: A system with charge (number of electrons) is placed in an electric field with potential E (volts).…
A:
Q: In a clamped frictionless pipe elbow (radius R) glides a sphere (weight W = mg) with zero initial…
A: Using Newtons law, we get,
Q: Consider the element of phase space defined by kinetic energy inter val S toʻstds. is the Volume in…
A: Consider phase space of particle in 3 dimensional space, which has 3 mometum directions and 3…
Q: What is the status of Gibbs paradox, introduced in classical thermodynamics? O Gibbs paradox has…
A: The Gibbs paradox refers to the apparent paradoxical increase in the entropy of an ideal gas upon…
Q: T04.2 Atoms in a harmonic trap We consider Nparticles in one dimension in an external potential,…
A:
Q: What does your result for the potential energy U(x=+L) become in the limit a→0?
A: We want to calculate lima→0qQ8πε0alnL+aL-a=qQ8πε0lima→0lnL+aL-aa
Q: q mass m. movesS in ene dimension Such that it has Lograngian the 12 ere v is differentiable…
A: Euler Lagrangian equation is given byL= m2x2.12+mx2 v(x)-v2(x). we have…
Q: Q2: A pendulum bob of mast m is suspended by a string of length / from a car of mass M which moves…
A: To determine: (a) The Lagrangian function The mass of the pendulum is m, the length of the pendulum…
Q: This is an integration problem, to calculate the center of mass (center of gravity) for a continuous…
A: Given: y(x)=hxl-12h=1.00 ml=3.00 m Also, the mass of the distribution can be calculated as:…
Q: Consider a Critically damped oscillater of m, damping 4ficient b, mas Co- Dand initial displadementA…
A: The energy of a damped oscillator is given by : E=12kAe-b2mt2Here, A is amplitude of oscillation…
Q: The equipartition theorem of energy in classical statistical mechanics says that the contribution to…
A:
Q: 35. COS Z
A:
Q: Let (Bt) be a Brownian motio 1. (B) I. (B?-t) I. (B?-3tB;) Iv. Z = B,ds
A: Given : B4 is an brownian motion. Let s < tE B4 | Bs = E B4-Bs | Bs + E Bs. | Bs…
Q: (i) Define the term ‘threshold frequency’ as used in photoelectric effect. (ii) Plot a graph showing…
A: Threshold frequency Threshold frequency is the minimum frequency…
Q: ii. The velocity potential for a two dimensional flow is 0 = x(2y-1). Determine the velocity at the…
A:
Q: What are the two major assumptions that are made in deriving the partition function for the ideal…
A: What are the two major assumptions that are made in deriving the partition function for the ideal…
Q: Problem 3.63. A person playing darts hits a bullseye 20% of the time on the average. Why is the…
A: The probability of hitting a bulls eye on a single throw is 0.2, and the probability of not hitting…
Q: a zero-mean white Gaussian noise with power spectral pass filter with bandwidth B. . Find the…
A:
Q: (a) In what way the kinetic energy is related to temperature? Is there any relation to the particle…
A:
Q: lculate the work for an ideal gas that expands isothermally at T0 from V1 to V2.
A:
Q: Let Ω be a new thermodynamic potential that is a “natural” function of temperature T, volume V, and…
A: Let Ω be a new thermodynamic potential that is a “natural” function of temperature T, volume V, and…
Q: Show that an irreversible isothermal expansion of an ideal gas against constant external pressure…
A: The ideal gas undergoes irreversible isothermal expansion against a constant external pressure. The…
Q: How will you express some state variables as partial derivatives of the Gibbs free energy G = U – TS…
A: The Gibbs free energy is given by, G=U-TS-YX State variables are the set of variables that describes…
Q: U = PV P = AT2 Find F0(U,V,N) and F1(U,V,N) After that use, Gibbs-Duhem to prove dF2=0 and…
A: We need to express F0 and F1 in terms of the extensive variables (U, V, and N) and the intensive…
Q: 1.7 Take U = U (T, P) and V = V (T, P). a. Show that - ),+"(),•[), +*(),]# OP ƏT OP dT b. Show that…
A: Given: U=UT,PV=VT,P
Q: Find the equilibrium positions of the following 1-dimensional potential energy function. Examine the…
A:
Q: Define poission bracket of two dynamical vari
A:
Q: = (V2)1/2 K πGOO ' Consider the dispersion relation of a linear spiral density wave perturbation…
A:
- Use a computer to reproduce the table and graph in Figure 2.4: two Einstein solids, each containing three harmonic oscillators, with a total of six units of energy. Then modify the table and graph to show the case where one Einstein solid contains six harmonic oscillators and the other contains four harmonic oscillators (with the total number of energy units still equal to six). Assuming that all microstates are equally likely, what is the most probable macrostate, and what is its probability? What is the least probable macrostate, and what is its probability?Coupled Harmonic Oscillators X2 :0 eeeee Leeee NM ) Write down the 2nd law for each of the masses. Use coordinates x, aud x, for m and M, and i,, *2 and a, a2. Hirnt: the force from spring I on monly depends on x, , but the ferce from spring 2 on m depand s on (x2-x,) two differantial 2) To simplify, let k, -k,k and m-M. Rewrite egg equatious from i) right above each other. your 3) Detine two new variables, X (Greek"chi") - x,+X2 and Ax = X,-x 2 two di ferential equations to produce Then add and subtract your very simple (harmanic) ones. 4) Write down the solutiou to bothe equations using Wask+2k2 ond evefficients A, B, C, and D two new , but w. : un 5) Now assune k-10k2 (this means that the two masses are "weakly coupled"). Also assume X,(0) = -10cm, x,(0)=0, xz (0)= o, x,(0)=0. Solve for A,B, C, D, and solve for x (t).Consider the dispersion relation w = is a positive constant. The phase and group velocity will be denoted by v and v, respectively. What is ak3, where a the ratio 9? 1 O 4 6.
- Lagrangian Dynamics O' A simple pendulum of mass m is piv- oted to the block of mass M, which slides on a smooth horizontal plane. O The mass M is connected to a spring of stiffness k, and the reference of poten- tial energy is at the smooth horizontal plane. ee 1. Find the velocity of mass m, w.r.t the origin O 2. Write the Lagrangian of the system 3. Derive the Euler Lagrangee equations 3.Consider N identical harmonic oscillators (as in the Einstein floor). Permissible Energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on. A) Calculating the selection function of a single harmonic oscillator. What is the division of N oscillators? B) Obtain the average energy of N oscillators at temperature T from the partition function. C) Calculate this capacity and T-> 0 and At T-> infinity limits, what will the heat capacity be? Are these results consistent with the experiment? Why? What is the correct theory about this? D) Find the Helmholtz free energy from this system. E) Derive the expression that gives the entropy of this system for the temperature.Charge is distributed over a triangular region in the xy-plane bounded by the y-axis and the lines y = 5 – x and y = 1+ x. The charge density at a point (x, y) is given by o(x, y) = x + y, measured in coulombs per square meter (C/m 2). Find the total charge. Select one: О а. 4 С b. 68 C 3 44 C 3 O c. O d. 20 37 C 3 е.
- Assuming a perfectly inelastic collision in one dimension, apply the principle of conservation of momentum to the following system:In the system in the initial state, cart A is launched at the speed (vi± delta vi) towards cart B, which is stationary.In the final state system, the two carts stick together and move together.The masses of the carts are known, as well as their uncertainty.Obtain a model for vf (the final speed of the carts) and its uncertainty based on known parameters only.Obtain a model for the relative kinetic energy loss (and its uncertainty) between the two states of the system: n=((Ki-Kf)/Ki )×100%. Simplify your expression as much as possible so that n (pronounced “eta”) only depends on the masses.mA= (0.47 ± 0.05)kg mB= (0.41 ± 0.02)kg initial velocity of cart A= (1.8 ± 0.04)m/sPlease answer both imagesSuppose f and g are differentiable functions with the values given below. f(5) = 1, f'(5) = 6, g(5) = -3, g' (5) = 2 Find h' (5) if h(x) = f(x).
- Consider a system of two Einstein solids, A and B, each containing10 oscillators, sharing a total of 20 units of energy. Assume that the solids areweakly coupled, and that the total energy is fixed. How many different microstates are available to this system?hey, please answer the question with all steps evident, and please answer them as simplistically as possible. also, part B has a typing error. it is meant to ask us for molar mass. not modular mass thank youLet p(x, y) be the joint probability distribution of the two random variables X and Y. Define the conditional entropy H(X | Y ) in terms of the joint distribution and associated conditional probabilities.