Question

Newton's law of cooling is: du/dt = -k (u-T) where u(t) is temperature of an object,...

Newton's law of cooling is: du/dt = -k (u-T) where u(t) is temperature of an object, t is in hours, T is a constant ambient temperature, and k is a positive constant.

Suppose a building loses heat in accordance with Newton's law of cooling. Suppose that the rate constant k has the value 0.15 hr^-1 . Assume that the interior temperature is Ti = 77F, when the heating system fails. If the external temperature is T = 5F, how long will it take for the interior temperature to fall to T1 = 35F?

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Question B: Newton's law of cooling states dθ/dt = −k (θ−T) where ? is the temperature...
Question B: Newton's law of cooling states dθ/dt = −k (θ−T) where ? is the temperature at time t, T is the constant surrounding temperature and k is a constant. If a mass with initial temperature, θ0, of 319.5 K is placed in a surroundings of 330.5 K, and k is 0.011 s-1 , what is its temperature after 4.7 minutes? Give your answer to 4 significant figures and remember to use units. ____________
(1 point) Newton's Law of Cooling states that the rate of cooling of an object is...
(1 point) Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose t is time, T is the temperature of the object, and Ts is the surrounding temperature. The following differential equation describes Newton's Law dT/dt=k(T−Ts), where k is a constant. Suppose that we consider a 95∘C cup of coffee in a 25∘C room. Suppose it is known that the coffee cools at a...
Newton’s law of cooling states that dx/dt = −k(x − A) where x is the temperature,...
Newton’s law of cooling states that dx/dt = −k(x − A) where x is the temperature, t is time, A is the ambient temperature, and k > 0 is a constant. Suppose that A = A0cos(ωt) for some constants A0 and ω. That is, the ambient temperature oscillates (for example night and day temperatures). a) Find the general solution. b) In the long term, will the initial conditions make much of a difference? Why or why not?
This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations...
This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 55°F. (a) Find a function T(t) that models the temperature  t hours after...
Newton's Law of Cooling tells us that the rate of change of the temperature of an...
Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation dTdt=k(T−A)dTdt=k(T-A), where TT is the temperature of the object after tt units of time have passed, AA is the ambient temperature of the object's surroundings, and kk is a constant of proportionality. Suppose that a cup of coffee begins at 179179 degrees and,...
dT/dt = k(T − A), where T is the temperature of the object, t is time,...
dT/dt = k(T − A), where T is the temperature of the object, t is time, k is the proportionality constant, and A is the constant ambient temperature. T (t) = A + Ce^kt is the general solution. Apply the solution to the following scenario: A Police Department officer discovered a corpse in a downtown alley at 1130pm on a night where the constant temperature was 40 degrees Fahrenheit. As she had been trained to do, she immediately recorded the...
Newton's law of cooling states that the temperature of an object changes at a rate proportional...
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the different between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 200 degrees F when freshly poured, and 1 min later has cooled to 190 degrees F in a room at 70 degrees F, determine when the coffee reaches a temperature of 150...
Newton’s Law of Cooling tells us that the time rate of chnge in temperature T(t) of...
Newton’s Law of Cooling tells us that the time rate of chnge in temperature T(t) of a body immersed in a medium of constant temperature A is proportional to the difference A − T.The DE modeling this is dT dt = k(A − T). A cup of hot chocolate is initially 170◦ F and is left in a room with an ambient temperature of 70◦ F. Suppose that at time t = 0 it is cooling at a rate of...
Newton’s law of cooling states that the rate of change of the temperature T of an...
Newton’s law of cooling states that the rate of change of the temperature T of an object is proportional to the temperature difference between the temperature S of the surroundings and the temperature T. dT dt = k(S − T) A cup of tea is prepared from boiling water at 100 degrees and cools to 60 degrees in 2 minutes. The temperature in the room is 20 degrees. 1. What will the temperature be after 15 minutes?
Newton’s Law of Cooling and the Ornstein-Uhlenbeck Process The Law of Cooling says the temperature difference...
Newton’s Law of Cooling and the Ornstein-Uhlenbeck Process The Law of Cooling says the temperature difference between an object (say a hot cup of coffee) and the ambient temperature (the temperature in the room) declines exponentially: If T(t) is the temperature of the object at time t, we have the ODE: d/dt(T(t) – Troom) = b (T(t) – Troom)    b < 0, Troom is a constant. Equivalently,   dT/dt = b (T – Troom) T(0) is the starting temperature of the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT