The conversion of cyclobutane (C,H3) to ethylene (CH4) is a first-order reaction. Thismeans that the concentration of cyclobutane at time t is given by In C = In Co – kt, where Cis the concentration at time t, Co is the initial concentration, t is the time since the reactionstarted, and k is the rate constant. Assume that Co = 0.2 mol/L with negligible uncertainty.After 300 seconds at a constant temperature, the concentration is measured to be C = 0.174+ 0.005 mol/L. Assume that time can be measured with negligible uncertainty.Estimate the rate constant k, and find the uncertainty in the estimate. The units of k willbe s-1.a.b.Find the relative uncertainty in k.The half-life t12 of the reaction is the time it takes for the concentration to be reducedto one-half its initial value. The half-life is related to the rate constant by t12 = (In 2)/k.C.Using the result found in part (a), find the uncertainty in the half-life.d.Find the relative uncertainty in the half-life.

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Answered: The conversion of cyclobutane (C,H3) to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) dT 1 and the temperature of the body. That is, = K[M(t) - T(t)], where K is a constant. Let K = 0.04 (min) and the temperature of the medium be constant, dt M(t) = 292 kelvins. If the body is initially at 360 kelvins, use Euler's method with h = 0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.
In Newton's law of cooling, the rate at which the temperature of an object is proportional to the difference between the temperature dT changes over time of the object T(t) and the temperature of the surrounding medium Tm. For the following problem, set up the initial value problem and then solve it. When a cake is removed from an oven, its temperature is 400° F. The room temperature is Tm later its temperature is 300° F. dt 65° F. Find the temperature function T(t) if three minutes
A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at timet (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt-and-water solution being poured into the tank alternately gets faster and slower. a) Show how the following differential equation describe the salt concentration s in the solution at any time t. Show full solution ds 0.2(1 + cos 2t)? dt
A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at time t (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt- and-water solution being poured into the tank alternately gets faster and slower. Determine which of the following differential equation describing the salt concentration S in the solution at any time t. O A. dS dt OB. dS dt OC. dS dt O D. dS dt = 0.2(1 + cos 21) ² = = = -0.2(1 + cos 21) ² 0.2 (1 + cos 21) ² 0.2 2 (1 + cos 21) ²
Consider a storage tank containing Vo liters of pure water. Water containing salt at a concentration of co kg/liter enters the tank at a rate r liters/min. The well-mixed solution leaves the tank at the same rate. Write down an initial value problem for the amount A(t) of salt in the tank at time t. You do NOT need to solve.

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