3. Determine expressions for q(m-1,n)→(m,n), q(m+1,n)→(m,n), q(m,n+1)→(m,n) and q(m,n-1)-(m,n), for conduction associated with a control volume that spans two different materials. There is no contact resistance at the interface between the materials. The control volumes are L units long into the page. Write the finite difference equation under steady-state conditions for node (m, n). Answer: N/A T→ T Ay Material A KA (m, n + 1) i (m1, n) (m, n) (m + 1, n) Material B (m, n1) | KB

Question 4: For the system shown in Figure 1: a) Find the transfer function G(s) = X(s)/F(s). b) Find 3, wn, %OS, T,, and T,. 28 N/m x(1) 5 kg f(1) 5 N-s/m Figure 1

Find the two-dimensional temperature distribution T(r,z) under steady state condition. Where, To=20 oC, TL=8200 oC. The density, conductivity and specific heat of the material are ρ =800 kg/m3, k=200 W/m.K, and cp=2500 J/kg.K, respectively. Also, r1=820 cm and L=1640 cm.

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Suppose that we have a wire (or a thin metal rod) of length that is insulated except at the endpoints. Let L denote the position along the wire and let t denote time. The 1- D heat equation is * temperature u 3 insulation O (a^2 u)/(at^2)=c^2 (a^2 u)/(ax^2) (a^2 u)/(at^2 )=c^2 du/əx au/Ət=c^2 (a^2 u)/(ðx^2 ) au/at=c^2 au/Əx none

. A transformation of 1 mole of an ideal gas is depicted in the figure below. Two paths are illustrated on the P-V diagram to take the gas from A to B through paths labelled a and 3. The points A and B lie on an isotherm with a temperature denoted by To. You can assume that the specific heat at constant pressure and specific heat at constant volume are both constants. Pressure Isotherm T = To A Path a 1 2 Path B B Volume (a) What is the net heat flow into, or out of, the gas for path a in terms of the temperature To and the temperature T₁ at the point 1. (b) What is the net heat flow into, or out of, the gas for path 3 in terms of the temperature To and the temperature T₂ at the point 2. (c) Under what circumstances will the heat flow along path o always be greater than that along path B

Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {Je1>, Je2>, Je3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H and the two operators B^ and D^ are defined by: 3 i 0 7 i 1- i 2a H= hwo -i 3 0 B= bo -i 7 1 + 2a 0. 0 2 1+i 1-i 6. 2a -3a where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: (ei|#(0) (e2l 4(0) e3| v(0)) |v(0)) = 3 Suppose that the initial state |U(0)> was left to evolve until t + 0. Q: After measuring operator D , the operator B was measured. What are the possible values of AB?

6. Rayleigh's method is based ONLY on potential energy of a number degree of freedom discrete system * Choose True False

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