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- The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P, has doubled in 7 years, how long will it take to triple? (Round your answer to one decimal place.) yr How long will it take to quadruple? (Round your answer to one decimal place.) yr еВookUse Newton's Law of cooling to determine the k value in air temperature of 40 degC. If 30 mins ago the boy was 120 degC and 10 mins age it was 80 degC. Select the correct response: 0.0321 -0.321 0.0235 -0.0235 none of the choicesThe left side of this equation tells how much energy Q the cylinder gives to the water while it cools. The right side of this equation tells how much energy Q the water and aluminum cup absorb from the cylinder to warm up. Because it is the same energy, they are equal. What is known in this equation? Mcyl 411.7 g, malum 46.5 g, malum+water = 175 g Can you find: mwater =? g Twater = Talum = 20°C (water and cup of room temperature) 90°C, T; = 35°C (hot cylinder and cool "cylinder+cup+water" temperatures) Tcyl kCal Calum = 0.22, Cwater 1 (specific heat of water and aluminum, measured in units kg-°C What are we looking for is Ccul - How we find it? Plug all the numbers into the equation (1), Ccul will be one unknown which you can calculate from the equation. Important, convert all the masses from grams to kilograms! After you find Ccyl, compare it to known value for the copper 0.093(our cylinder is made out of copper). |Ceyl -0.093| % : · 100% 0.093
- Q8): To find how much heat is required to bring a kettle of water to its boiling point, you are asked to calculate the specific heat of water at 61°C. The specific heat of water is given as a function of time in Table below. Temperature, T Specific heat, C₂ (°C) J kg-°C 22 42 52 82 100 4181 4179 4186 4199 4217 Determine the value of the specific heat at 7=61°C using the direct T method of interpolation and a third order polynomial. Find the absolute relative approximate error for the third order polynomial approximation (Lagrange Method).The following diagram illustrates measurements that 145.0 L 0 d. Q Joom ма 8-42.00 で how equal to I'm in Thermal conductivity. materi di L M Heat Flow ? b. 3.24 kW N 0 d २ R I. thermal Resistance 17 a. 0.80 KW b. none OF c. 9.25 KIKW d. 1.08 e. K| kw 0.68 44.12 KW 37.5 KW M R 1.0m the above d mall a. decrease b. unchanged c. increase the walls side is exposed to temperatures of 5000 upper while its lower siche is exposed to unidirectional heat flow in Assume steady state, radiation and Convectim heat effects. 20°C. y direction Neglect none of IF antract reere tance heat N S 1.0m op the above a row of bricks, an taking thicknees Bricks k (kw/m-k) Flow? 0.50 0.25 0-50 0-80 0.4⁰ 0.50 0.25 0.50 • not neglighe, what happen to overall d. inereact then decrease e increase / decrease depending on value of Contact resistanceThe heat transfer conducted through material is calculated from the equation: Q = KX AXTD/L Where K: Conductivity of material A: Area of heat transfer TD: Temperature difference across material L: Thickness of material A student measures the area, thickness and temperature difference and assumes that the error in conductivity is negligible. The student also estimates the uncertainty range for each variable. In estimating the maximum possible value of Q, the student should use the following formula: A B Q max= K x A max x TD max / L max Q max= K x A max x TD max / L nom Q max= Q nominal + dQ/dLmin Q max= K x A max x TD max / L min
- The 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) StrainSuppose that the population P(t) of a country satisfies the differential equation dP = kP(1200 – P) with k constant. Its population in 1960 was 300 million and was dt then growing at the rate of 2 million per year. Predict this country's population for the year 2010 This country's population in 2010 will be million. (Type an integer or decimal rounded to one decimal place as needed.)Two kinds of bacteria are found in a sample of tainted food. It is found that the population size of type 1, N1 and of type 2, N2 satisfy the equation dN/dt=-0.1/N1 dN/dt30.7/N2 N1 is equal to 1000 at time equal to zero, while N2 is equal to 30 at time equal to zero. Then the population sizes are equal N1 = N2 at what time? (4 decimal places)
- Newtons laws of cooling proposes that the rate of change of temperature is proportional to the temperature difference to the ambient (room) temperature. And can be modelled using the equation: dT/dt = -k (T-Ta)It can also be written as dT/T-Ta = -k dtWhere:T = Temperature of materialTa = Ambient (room) temperaturek = A cooling constanta) integrate both sides of the equation and show that the temperature difference is given by:(T-Ta) = CoE^-kt(Co is a constant for this problem)B) calculate Co if the initial temperature is 70 degrees C and Ta = 20 degrees C?Consider a process to prepare a metal for a certain application. There are five parameters that must be considered: temperature, quenching rate, cooling time, carbon content, CO₂ concentration. It is desired to determine which of these parameters has the most influence on the process. There are two levels for each parameter as shown below. Temperature (°C) Quenching Rate(°C/s) Cooling time (s) Carbon Content (wt% C) CO₂ Concentration (%) Eight experiments were defined as follows: Experiment Carbon Content (wt% C) 1 2 3 4 5 6 7 8 1) What size orthogonal array should be used for evaluation (assume noise is negligible)? 2) Generate the array with the level values (i.e. Level 1 and Level 2). 1 1 1 1 6 6 6 6 Quenching Rate (°C/s) 35 35 140 140 35 35 140 140 Four trials were run for the experiments defined above: Experiment 1 2 3 4 5 6 7 8 Level 1 760 35 1 1 5 T1 68.00 69.84 74.36 71.71 91.27 54.39 64.65 60.31 Cooling Time 1 1 300 300 300 300 1 1 T2 61.41 64.76 61.30 58.42 90.89 Level 2 900…Mechanical Engineering The fatigue strength limit Sn (n = 106) of a steel part is 112 MPa and its ultimate tensile strength (Sy) is 385MPa. Adopting Ct = 1, and S103 = 0.9 * Su* Ct, determine: (Use two decimal places in the answers), (* is multiplication signal): a) The fatigue strength (in MPa) corresponding to a life of 40000 cycles. b) The average life in cycles that this part would last if subjected to an alternating stress of 170 MPa due to bending.