Question

**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, θ_{0}, 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.

____________

Answer #1

(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 is: du/dt = -k (u-T) where u(t) is
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Newton’s law of cooling states that the rate of change of the
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The temperature in the room is 20 degrees. 1. What will the
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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
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night and day temperatures). a) Find the general solution. b) In
the long term, will the initial conditions make much of a
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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
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dT/dt=k(T−Ta)
where k<0.
When a coil of steel is removed from an annealing furnace its
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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...

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
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(a) Find a function T(t) that models the
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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
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If the body is initially at 360 kelvins, use Euler’s...

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
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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
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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...

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