2. Use the convolution integral method to derive expressions for the response of an undamped system subjected to the forcing function shown in Figure 2. F(1) F₁ 0 F₁(1-cos 210 Figure 2
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- 5.7 In a continuous agitation heating tank, w=wi=200lb/min, Cp and density are constant, the volume of the heating tank V=1.63ft^3, the specific heat of the liquid is 0.32Btu/(lbF), and the density is 62.4lb/ft^3 am. The heat input Q from the heater is 1680 Btu/min, and the inflow temperature is maintained at 80F. (a) Find the response when the inlet temperature suddenly decreases to 65F.Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are ρ =1200 kg/m 3, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux q =1000 W/m 2 is applied to the upper surface. The right and left surfaces are also kept at 0oC. Bottom surface is insulated.Use the Dahamel integral method to derive expressions for the response of an undamped system subjected to the forcing functions shown in Figs. 4.46(a) to (c).
- If a system is subjected to a suddenly applied non-periodic force, the answer is: a) constant b) transient c) periodicif a 136.51g Al rod (c=0.900 j/g°C) is at 100.0°C and placed into 250.0g of water at 21.8°C, what is the temperature of the system (rod + water) at equilibrum assuming no losses to the surrounding? a) 46°Cb) 30°Cc) 206°Cd) 18°CFind 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.
- A certain ideal gas (unknown) inside a close piston-cylinder assembly undergoes a set of processesthat composed of Isothermal expansion from State point 1 to state point 2, Isometric heat rejectionfrom state point 2 to state point 3, and Isentropic compression from state point 3 back to the initialcondition. If the maximum pressure is 3000kPa and maximum and minimum volume is 200cm3and50cm3, analyze the problem and perform the following:a. Draw and label the graph of this set of processes in the P-V and T-S diagram showing the statepoint numbers and energy directions.b. From the known ideal gases as shown in Table 1.0, select the best suited ideal gas to attain theprocesses stated if the lowest pressure is limited to 629.8kPa. Assume a constant specific heat.c. For the selected ideal gas from b, compute the work of compression (kJ/kg), work of expansion(kJ/kg), and heat rejected (kJ/kgA certain ideal gas (unknown) inside a close piston-cylinder assembly undergoes a set of processesthat composed of Isothermal expansion from State point 1 to state point 2, Isometric heat rejectionfrom state point 2 to state point 3, and Isentropic compression from state point 3 back to the initialcondition. If the maximum pressure is 3000kPa and maximum and minimum volume is 200cm3and50cm3, analyze the problem and perform the following: a. Draw and label the graph of this set of processes in the P-V and T-S diagram showing the statepoint numbers and energy directions. b. From the known ideal gases as shown in Table 1.0, select the best suited ideal gas to attain theprocesses stated if the lowest pressure is limited to 629.8kPa. Assume a constant specific heat. c. For the selected ideal gas from b, compute the work of compression (kJ/kg), work of expansion(kJ/kg), and heat rejected (kJ/kg)A cup of coffee with cooling constant k = 0.09 min- 1 is placed in aroom at temperature 20°C.(a) How fast is the coffee cooling (in degrees per minute) when its temperature is T = 80° C?(b) Use the Linear Approximation to estimate the change in temperatureover the next 6 s when T = 80°C.( c) If the coffee is served at 90°C, how long will it take to reach an optimaldrinking temperature of 65°C?
- The Born–Oppenheimer principle [1] is often said to be a prerequisite for the concept of a PES. Yet the idea of a PES [2] predates the Born–Oppenheimer principle (1927), DiscussThe reaction 2I- (aq) + S2O82- (aq) → I2 (aq) + 2SO42- (aq) was studied at 25°C. The following results were obtained where Rate = - (Δ[S2O82-])/(Δt) [I-]0(mol/L) [S2O82-]0(mol/L) Initial Rate (mol/L ·s) 0.080 0.040 12.5 x 10-6 0.040 0.040 6.25 x 10-6 0.080 0.020 6.25 x 10-6 0.032 0.040 5.00 x 10-6 0.060 0.030 7.00 x 10-6 a. Determine the rate law. b. Calculate a value for the rate constant for each experiment and an average value for the rate constant*Need answer only for the a3. Consider a mass spring system with an external force ?(?) = ?osin?o?. Let's assume ? is the mass of the object attached to the spring, ? is the spring constant, and ? is the damping coefficient. Let's also assume that ?(0) and ?′(0) are the location and speed of the object attached to the spring at time ? = 0. a) Find the general solution of the differential equation governing the motion of the spring, in terms of ?,?,?,?(0),?"(0),?0 and ?0. Your solution shall cover all possible cases including 1. the case with no damping and ?! is not equal to natural frequency of the system, ? =sqrt?/?. 2. the case with no damping and ?! is equal to natural frequency of the system, ? =sqrt?/?. 3. the three cases with damping (overdamped, critically damped, and underdamped).