2. Derive expressions for the isothermal compressibility below and above T. Approach the critical...
Problem 1 CH7/5pts Warm up. Show that: 1. PK 1- P ()where is the isothermal compressibility 2. PB 1+T (n)pwhere B is the thermal expansion. р' 3. Show that Te, Pe and Vm.e in a system described by a van der Waals equation of state depend only on a and b parameters.
2) Use the Duhamel integral method to derive the expressions for the response of the undamped system subjected to the forcing functions shown in fig A. Set up the expression for x[t) in fig. B Ft 0.sto MA 2+ 0.5 € Fig A
Derive expressions for a Fermi gas in 2-D box of area A for the following: (a) The Fermi energy aSEF-n2/(4πm) (N/A). (b) The T-O energy as U-1/2 N EF (c) Density of states g(e) N/EF (d) Solve N-J g(ε) nFD(ε)de (where the integral goes from 0 to 00) for the chemical potential, μ(T), and show that the chemical potential recovers kT>XE (classical) and kT<< ε,degenerate Fermi gas) limits. Derive expressions for a Fermi gas in 2-D box of area A...
For the circuit shown below do the following: 1. Find expressions for vc(t) and i(t) for t 2 0. а. Find an expression for the power to the resistor, pR(t) b. Integrate the power to the resistor from t = 0 to co. С. d. Show that the total energy to the resistor is equal to the energy stored in the capacitor at t 0 Determine the time at which Vc(t) 25 V? е. t 0 i(t) vc(t) 2 HF...
6. In the circuit below, the voltage and current expressions are i = 64e-10t A, t 2 0 0 Find a) R. b) t(in milliseconds ms) c) L d) The initial energy stored in the inductor e) The time (in milliseconds) it takes to dissipate 60% of the initial stored energy.
Considering the above system determine the following information 21 (15) 22 Derive the equation of deflection of the beam using the second order flexural equation EL = M(I), Utilize your previously derived solution to obtain the beam deflection dg at the (5) point B where I = 0; Utilize your previously derived solution to obtain the beam rotation Og at the (5) point B where I = 0, 23 Total Marks: [25] Hints for Question 2 (i) You can assume...
Problem 1 (Section 6.3) Starting with the finite difference expressions for the partial derivatives, re-derive the forward Euler method for the heat equation with an extra nonlinear term: u(0,t)- u(1t)-0 Then, find the solution over three time steps (i.e. find the twelve vawith 3 decimal digits of precision, assuming k = 1, γ=2, M = 0.01, L = 1 and N=5, with initial condition u a table to show your results. It is strongly recommended that you write a short...
Please provide any MATLAB code you used for plotting. 1 1 2 m2 1. Consider the system above. Derive the equation of motion and calculate the mass and stiffness matrices. a) Calculate the characteristic equation forthe case m 9 kg m 1 kg k 24 N/m k2 3 N/mk3- 3 N/m and solve for the system's natural frequencies. b.) Calculate the eigenvectors u1 and u2 c.) Calculate xi(t) and x2(t), given x2(0)-1 mm, and xi(0) - vz(0) -vi(0) 0 d.)...
A gas cylinder containing carbon dioxide, CO2, 85% by volume, and nitrogen, N2, 15% by volume has a volume of 2.2 m and is kept at a temperature of 20°C. You may assume the gas mixture is ideal. 0 Calculate the pressure in kPa in the cylinder when it contains 50 kg of gas. [2 marks] After a certain amount of gas has been used, the pressure decreases by 150 kPa. Calculate the mass of gas used. [2 marks] (b)...
Problem 2 (3 marks) There are 2 point charges Qt) at (1,0,0) and Q2(t) at (-0.5, 0, 0). Given current I flows from Q2t) to Qı(t) Find the line integral of H along the square close path C crossing (0,-1,1), (0,1,1), (0,1,-1), (0,-1,-1). Problem 2 (3 marks) There are 2 point charges Qt) at (1,0,0) and Q2(t) at (-0.5, 0, 0). Given current I flows from Q2t) to Qı(t) Find the line integral of H along the square close path...