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Please provide a step by step process on how to get the answer. Thank you. The a

ID: 1332220 • Letter: P

Question

Please provide a step by step process on how to get the answer. Thank you.

The apartments in a building have central heating/cooling systems that are controlled individually. The controls are designed so that heating or cooling will adjust the temperature according to dT / dt (t) = -k (T(t) - Ta), where T degree a F is the desired temperature in the apartment. Assume that the temperature is initially at T degree 1 F and show that the temperature will return back to T degree a F in time. Unfortunately, the electrician wired the controls incorrectly for two apartment adjacent to teach other. The control in apartment A responds to the temperature TB(t) degree F in the apartment next door, and vice versa. Thus, dTA / dt (t) = - k(TB(t) - T a), dTB / dt (t) = -k (TA (t) - T a). Obtain a single differential equation for TA(t) degree F and construct a general solution. Suppose the temperatures have the initial values TA(0) = T degree 1 F and T B (0) = T degree 2 F and determine the role of the initial values on the long term behavior of the system. Suppose k = 0.5 per hr and the control temperature is T a = 72 degree r F . Let T B be at the control temperature T a initially, but assume the temperature T A (0) = 71 degree F. Determine the temperature T A after 10 hrs.

Explanation / Answer

let d be the distance between the plates


the field will do work on the charge in opposite direction


the proton has to move a diatance of d/2


the work done by the elctric field = W = E*q*d/2


E = V/d

W = V/d*q*d/2 = Vq/2 = (500*1.6*10^-19)/2 = 4*10^-17 J


the kinetic energy of the proton

KE = 0.5*m*v^2 = 0.5*1.67*10^-27*(2*10^5)^2 = 3.34*10^-17 J

KE of the proton is not equal to the work


that means the proton is not having suffucuent energy to reach positive plate


part(d)

work done = potntial difference between the mid point and negative plate* charge

W = (V/2)*q


KE at the mid point KE1 = 0.5*m*v1^2

KE at the negative plate = KE2 = 0.5*m*v2^2


W = dK

(v/2)*q = 0.5*m*(v2^2 - v1^2)

(500/2)*1.6*10^-19 = 0.5*1.67*10^-27*(v2^2-(2*10^5)^2)


v2 = 2.96*10^5 m/s <<<----answer

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