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5.8 Show that for temperatures well below e,, the mean free path of a phonon can...
Consider the phonon dispersion relation for a 10cm long GaAs crystal, shown in the figure below....
Consider the phonon dispersion relation for a 10cm long GaAs
crystal, shown in the figure below.
(a) How can you obtain the phonon speed from the dispersion
relation? What is the speed of the phonons with the shortest
wavelength? (2 marks) (b) Which is more effective at carrying
energy across a solid: long wavelength or short wave- length
phonons? Why? (2 marks) (c) What is the wavelength of the
fundamental mode of this crystal? (1 mark) (d) In the long...
(a) Show that for a gas, the mean free path between collisions is related to the...
(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...
Problem 3 - Mean free path (8 marks) Let's assume the opacity inside of a star...
Problem 3 - Mean free path (8 marks) Let's assume the opacity inside of a star is constant. The optical depth is T = not where o is the collisional cross-section of an ion. If the optical depth is T = 1, then the photon can't go very far before it's scattered. We write the mean free path as L which is the average distance a photon can go before being scattered. a. If the conditions in the Sun have...
Viterbi algorithm We can use dynamic programming on a directed graph G = (V, E) for...
Viterbi algorithm We can use dynamic programming on a directed graph G = (V, E) for speech recognition. Each edge (u, v) in E is labeled with a sound s(u, v) from a finite set S of sounds. The labeled graph is a formal model of a person speaking a restricted language. Each path in the graph starting from a distinguished vertex v0 in V corresponds to a possible sequence of sounds produced by the model. The label of a...
2. Show that the thermal efficiency for the gas power plant shown below can be expressed as follo...
2. Show that the thermal efficiency for the gas power plant shown below can be expressed as follows k-1 +1 where nc and nt are the isentropic efficiencies of the compressor and turbine, respectively. Ts and Tı are the maximum and minimum temperatures of the cycle, respectively; rp is the pressure ratio of the cycle and k is the ratio of specific heats. Assume specific heat capacity to be constant for this derivation. (6 Points) Heater 3 Work 2 Heat...
you can skip #2 Show that F() = Vf (), 1. Let F R3 -R be defined by F(I) = F12", where u where f(r,y,) = =- +22...
you can skip #2
Show that F() = Vf (), 1. Let F R3 -R be defined by F(I) = F12", where u where f(r,y,) = =- +22 2. Consider the vector field F(E,) = (a,y) Compute the flow lines for this vector field. 3. Compute the divergence and curl of the following vector field: F(x,y,)(+ yz, ryz, ry + 2)
Show that F() = Vf (), 1. Let F R3 -R be defined by F(I) = F12", where u...
Question 10 RD 1 (X-μ)/μ|. Show that (5.28) 9. See Problem 5.8. Compute the signal-to-noise ratio...
Question 10
RD 1 (X-μ)/μ|. Show that (5.28) 9. See Problem 5.8. Compute the signal-to-noise ratio r for the random variables from the fol. lowing distributions: (a) P(A), (b) E(n, p), (c) G(p), (d) Γ(α, β), (e) W (α, β), (f) LNue). and (g) P(α,0), where α > 2. 10. Let X and F be the sample means from two independent samples of size n from a popu- lation with finite mean μ and variance σ. Use the Central Limit...
Standard free energy change (Delta degree G) and cell potential (E degree) can be said to...
Standard free energy change (Delta degree G) and cell potential (E degree) can be said to measure the same thing and are convertible by the equation: Delta G degree = nF E degree _cell where n is the total number of moles of electrons being transferred, and F is Faraday constant 9.6- 1853415 times 10^C/mol. The free energy (Delta G degree) of a spontaneous reaction is always negative. For each of the electrochemical cells below, calculate the free energy of...
can you show the correct R/S stereochemistry with priorities for all structures as well as E/Z where it is possible....
can you show the correct R/S stereochemistry with priorities
for all structures as well as E/Z where it is possible.
Он CH3 "CНз но" NH но -CНз 7 14 H2N NH2 NH2 о 1 НCN NH О Нас Но :о S NH HN NH2 10 ОН 14 ZI
Он CH3 "CНз но" NH но -CНз 7 14 H2N NH2 NH2 о 1 НCN NH О Нас Но :о S NH HN NH2 10 ОН 14 ZI
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose...
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose response is governed by the following constant-coefficient, is performing underdamped free vibrations if oc 1 (underdamped ). (Seetion 6.7). linear, 2td order, ODE ) and 1t)- (freei (a) After assuming a solution t)et where C and p are conustants, show every step that proves yit) can be expressed in terms of the yet-to-be-determined constants A and B and he constant wa (defined above) called...
Consider the phonon dispersion relation for a 10cm long GaAs
crystal, shown in the figure below.
(a) How can you obtain the phonon speed from the dispersion
relation? What is the speed of the phonons with the shortest
wavelength? (2 marks) (b) Which is more effective at carrying
energy across a solid: long wavelength or short wave- length
phonons? Why? (2 marks) (c) What is the wavelength of the
fundamental mode of this crystal? (1 mark) (d) In the long...
(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...
Problem 3 - Mean free path (8 marks) Let's assume the opacity inside of a star is constant. The optical depth is T = not where o is the collisional cross-section of an ion. If the optical depth is T = 1, then the photon can't go very far before it's scattered. We write the mean free path as L which is the average distance a photon can go before being scattered. a. If the conditions in the Sun have...
2. Show that the thermal efficiency for the gas power plant shown below can be expressed as follows k-1 +1 where nc and nt are the isentropic efficiencies of the compressor and turbine, respectively. Ts and Tı are the maximum and minimum temperatures of the cycle, respectively; rp is the pressure ratio of the cycle and k is the ratio of specific heats. Assume specific heat capacity to be constant for this derivation. (6 Points) Heater 3 Work 2 Heat...
you can skip #2
Show that F() = Vf (), 1. Let F R3 -R be defined by F(I) = F12", where u where f(r,y,) = =- +22 2. Consider the vector field F(E,) = (a,y) Compute the flow lines for this vector field. 3. Compute the divergence and curl of the following vector field: F(x,y,)(+ yz, ryz, ry + 2)
Show that F() = Vf (), 1. Let F R3 -R be defined by F(I) = F12", where u...
Question 10
RD 1 (X-μ)/μ|. Show that (5.28) 9. See Problem 5.8. Compute the signal-to-noise ratio r for the random variables from the fol. lowing distributions: (a) P(A), (b) E(n, p), (c) G(p), (d) Γ(α, β), (e) W (α, β), (f) LNue). and (g) P(α,0), where α > 2. 10. Let X and F be the sample means from two independent samples of size n from a popu- lation with finite mean μ and variance σ. Use the Central Limit...
Standard free energy change (Delta degree G) and cell potential (E degree) can be said to measure the same thing and are convertible by the equation: Delta G degree = nF E degree _cell where n is the total number of moles of electrons being transferred, and F is Faraday constant 9.6- 1853415 times 10^C/mol. The free energy (Delta G degree) of a spontaneous reaction is always negative. For each of the electrochemical cells below, calculate the free energy of...
can you show the correct R/S stereochemistry with priorities
for all structures as well as E/Z where it is possible.
Он CH3 "CНз но" NH но -CНз 7 14 H2N NH2 NH2 о 1 НCN NH О Нас Но :о S NH HN NH2 10 ОН 14 ZI
Он CH3 "CНз но" NH но -CНз 7 14 H2N NH2 NH2 о 1 НCN NH О Нас Но :о S NH HN NH2 10 ОН 14 ZI
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose response is governed by the following constant-coefficient, is performing underdamped free vibrations if oc 1 (underdamped ). (Seetion 6.7). linear, 2td order, ODE ) and 1t)- (freei (a) After assuming a solution t)et where C and p are conustants, show every step that proves yit) can be expressed in terms of the yet-to-be-determined constants A and B and he constant wa (defined above) called...
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