Question

(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 rate of 2∘C/min. when it is 70∘C. Answer the following questions.

1. Find the constant k in the differential equation. Answer (in per minute): k=

2. What is the limiting value of the temperature? Answer (in Celsius): T=

3. Use Euler's method with step size h=2 minutes to estimate the temperature of the coffee after 1010 minutes. Answer (in Celsius): T(10)≈

Answer #1

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,...

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 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/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...

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.
____________

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...

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...

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...

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 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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 27 minutes ago

asked 50 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 4 hours ago

asked 4 hours ago

asked 4 hours ago