Question

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?

Math   Calculus   
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
15. Newton’s Law of Cooling. Newton’s law of cooling states that the rate of change in...
15. Newton’s Law of Cooling. 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) and the temperature of the body. That is, dT/dt = K[M(t) - T(t)] , where K is a constant. Let K = 0.04 (min)-1 and the temperature of the medium be constant, M(t) = 293 kelvins. If the body is initially at 360 kelvins, use Euler’s...
(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/heating states that the time rate of change of temperature of a cooling/heating...
Newton's law of cooling/heating states that the time rate of change of temperature of a cooling/heating object is proportional to the difference between the temperature of the object and the ambient temperature of the medium where the object resides. If we let Ta represent the ambient temperature and T represent the temperature of the object then a DE representing this situation is dT/dt=k(T−Ta) where k<0. When a coil of steel is removed from an annealing furnace its temperature is 684...
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,...
This question is about Newton’s law of cooling, which states that the temperature of a hot...
This question is about Newton’s law of cooling, which states that the temperature of a hot object decreases proportionally to the difference between its temperature and the temperature of the surroundings. This can be written as dT dt = −k(T − Ts), where T is the temperature, t is time, k is a constant and Ts is the temperature of the surroundings. For this question we will assume that the surroundings are at a constant 20◦ and A that the...
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 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 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...
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?
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. ____________
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT