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Concept explainers
Given the data below, find the isothermal work done on the gas as it is compressed from 23 L to 3 L
V, L | 3 | 8 | 13 | 18 | 23 |
P, atm | 12.5 | 3.5 | 1.8 | 1.4 | 1.2 |
(a) Find the work performed on the gas numerically, using the 1-, 2-, and 4-segment trapezoidal rule.
(b) Compute the ratios of the errors in these estimates and relate them to the error analysis of the multiple-application trapezoidal rule discussed in Chap. 21.
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Chapter 24 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- 2. In class, we derived an expression for hR/RT for a gas that obeyed the Pressure Explicit Virial Expansion truncated after the third term. In class, we assumed that B and C were not functions of temperature. a. Please rework the derivation with B = B(T) and C = 0. b. Please continue the derivation under the assumption that B(T) = mT + b. Where m and b are the slope and y-intercept of a straight, respectively. %3Darrow_forwardnumber 1 A food product containing 80% moisture content is being frozen. Estimate the specific heat of the product at -8 ° C when 80% of the water is frozen. The specific heat of the dry product is 2 kJ / (kg ° C). It is assumed that the specific heat of water at -10 ° C is the same as the specific heat of water at 0 ° C, and that the specific heat of ice follows the function Cp es = 0.0062 T Frozen + 2.0649. Cp of frozen product = kJ / kg ° C.arrow_forwardA:YV 36 ll 46.ll Test 3.pdf F1 F2 a F3 A d. C a F4 E Consider the following values: - F5 a = 12 m; b = 10 m; c = 10 m; d = 8 m; F1 = 6 kN; F2 = 7 kN; F3 = 8 kN; F4 = 9 kN; F5 = 10 kN; a = 30° 0 = 45° B = 60° 1] What is the resultant moment of the five forces acting on the rod about point A? a) - 111.6 kN.m b) 112.6 kN.m c) - 184.6 kN.m d) - 109.6 kN.m e) - 104.1 kN.m f) None of them 2] What is the resultant moment of the five forces acting on the rod about point B? a) -95.8 kN.m b) 42.7 kN.m c) 80.9 kN.m d) 10.9 kN.m e) 51.8 kN.m f) None of them 3] What is the resultant moment of the five forces acting on the rod about point C? a) 32.6 kN.m b) - 21.1 kN.m c) 17.4 kN.m d) - 16.5 kN.m e) 15.6 kN.m f) None of them 4] What is the resultant moment of the five forces acting on the rod about point D? a) 37.6 kN.m b) 73.8 kN.m c) 71.6 kN.m d) 52.1 kN.m e) 21.1 kN.m f) None of them 5] What is the moment of the force F2 about point E? a) 90.7 kN.m b) - 88.1 kN.m c) 54.6 kN.m d) 103.1 kN.m e)…arrow_forward
- Here I'm finding final kinetic energy KE2, given initial kinetic energy, initial force, alpha N/m^3 and beta N representing F(x). I integrated F(x)dx though I'm not sure how to integrate Fo with respect to X. I tried just finding the integrand ouput of 7.5x10^4m and subtracting the initial force, since the initial force would count as x=0, or I assumed. I then followed the regular approach of adding over the initial KE1 to isolate the unknown KE2 which I keeo getting as 1.07x10^10 which seems to be off. Again, I suspect where I'm going wrong is integrating the initial force -3.5x10^6N with respect to x, but other than what I've already done, that doesn't make sense to me.arrow_forwardThe following related values of the pressure p in kN/m2 and the volume V in cubic meter where measured from the compression curve of an internal combustion engine indicator diagram. Assuming that P and V are connected by the law PVn: C, find the value of n. p 3450 2350 1725 680 270 130 V .0085 .0113 .0142 .0283 .0566 .0991arrow_forwardThe stress profile shown below is applied to six different biological materials: Log Time (s] The mechanical behavior of each of the materials can be modeled as a Voigt body. In response to o,= 20 Pa applied to each of the six materials, the following responses are obtained: 2 of Maferial 6 Material 5 0.12 0.10 Material 4 0.08 Material 3 0.06 0.04 Material 2 0.02 Material 1 (a) Which of the materials has the highest Young's Modulus (E)? Why? Log Time (s) (b) Using strain value of 0.06, estimate the coefficient of viscosity (n) for Material 6. Stress (kPa) Strainarrow_forward
- PROBLEM #1: Complete the data of the table below. Copy the entire table in your paper and use a different colored pen for your answers, you may also box your answers. Show solution. T:K P: kPa H: kJ/kg U: kJ/kg State (if wet steam provides xv as well) 1 525 350 2 125 2700 3 455.15 750 4 600 Xv = 0.8 5 200 1800 PROBLEM #2 A nozzle is used to increase the velocity of steam before it enters a turbine as a part of a power plant. The steam entering is at 1 MPa, 500 K and leaves at the conditions of 350°C and 2 MPa. If the nozzle has an inlet diameter of 3 cm and an outlet diameter of 1 cm, how much is transferred during the process? Is it lost or gained?arrow_forward3. A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an expression for the temperature u(x, t) if the bar is made of cast iron. Material a (cm²/s) Silver 1.71 Copper 1.14 Aluminum 0.86 Cast iron 0.12 Granite 0.011 Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materialsarrow_forward22°F Clear 1MMBU BU ► ► ► 20°HD®°°*EqqaHÛDin × ODE DDE DE DE File C:/Users/ignor/Downloads/Assignment%203%20(2).pdf T❘ Read aloud Ask Copilot Draw a) Use Newton's second law b) Use the Torque equation /// Collar A is free to slide with negligible friction on the circular guide mounted in a vertical frame. Find the EOM of collar A if the frame is given a velocity v and a constant horizontal acceleration a to the right. Search 1 A www of 6 TTTT | CD a laaa 8 o + ENG 60 T N 7:35 PM 1/17/2024 xarrow_forward
- number 1 A food product containing 75% moisture content is being frozen. Estimate the specific heat of the product at -10° C when 85% of the water is frozen. The specific heat of the dry product is 2 kJ / (kg ° C). It is assumed that the specific heat of water at -10 ° C is the same as the specific heat of water at 0 ° C, and that the specific heat of ice follows the function Cp es = 0.0062 T Frozen + 2.0649. Cp of frozen product = kJ / kg ° C.arrow_forwardCreep exercises The following data in the table below was obtained a from rupture test. Stress (MPa) Temperature (°C) Rupture time (hr) T 550 580 0.75 550 555 5.5 550 540 19.2 550 525 62.0 70 760 2.05 70 730 8.2 70 700 36.5 70 675 134 Assume: C = 46 Establish whether the Larson-Miller parameter is valid for both stresses (550 and 70 MPa). Was there a change in creep mechanism when changing the stress from 550 to 70 MPa during rupture test? Motivate your answer with the aid of calculation.arrow_forwardQ7// State the Cowper-Symonds empirical equation which describes the effect of strain rate on the flow stress of metallic materials. Using the Cowper-Symonds equation, together with the material constants D and q in the equation as given in the Table below, describe the comparative high strain rate sensitivity of the different materials (assume e° = 3 4 s'). Material D (s') Copper 4.8 52 Stainless Steel 9.2 99 Titanium Alloy 9.2 122 Aluminium Alloy 4.2 6710 Mild Steel 5.1 45arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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