Question

Suppose a cup of coffee is at 100 degrees Celsius at time t=0, it is at 70 degrees at t=15 minutes, and it is at 45 degrees at t=30 minutes. Compute the ambient temperature.

Answer #1

A cup of coffee at 90 Celsius is put into a 20 Celsius room,
t=0. The coffee's temperature is changing at a rate of r (t) =
-7(0.7^t) Celsius per minute, with t in minutes. Estimate the
coffees temperature when t=10.
Round answer to TWO decimal places:

If a cup of coffee has temperature 100°C in a room where the
ambient air temperature is 21°C, then, according to Newton's Law of
Cooling, the temperature of the coffee after t minutes is T ( t ) =
21 + 79 e − t / 45 . What is the average temperature of the coffee
during the first 14 minutes?

A cup of coffee has a temperature of 200F. It is placed in a
room that has temperature 70 F. After 15 minutes, the temperature
of the coffee is 150F.
a) Model the temperature of the cup of coffee at time t.
b) How long will it take for the coffee to cool down to 100◦
F?

Suppose a cup of coffee is 160 degrees right after the coffee is
poured. You are only comfortable drinking coffee when it cools to
120 degrees. You check after five minutes, and the coffee is still
hot (135 degrees!). When will you be able to first comfortably sip
the coffee? Note: The equation for Newton’s law of cooling is ?? =
? (? − ??); its solution is:T(t) = Ts + (T0 – Ts) e^kt. Assume the
surrounding temperature is...

Calculate the pH of a 0.0322M KOH solution at each
temperature.
0 degrees Celsius pH=
50 degrees celsius pH=
T (°C)
Kw
0
1.15 × 10–15
5
1.88 × 10–15
10
2.97 × 10–15
15
4.57 × 10–15
20
6.88 × 10–15
30
1.46 × 10–14
35
2.07 × 10–14
40
2.88 × 10–14
45
3.94 × 10–14
50
5.31 × 10–14
100
5.43 × 10–13

In 1701, Issac Newton proved his Law of Cooling: T(t)
=Aekt +Ta, which is an exponential model that
relates the temperature of an object T as a function of
time t (we will use minutes) that is placed in an
environment with ambient temperature Ta.
Suppose a cup of hot coffee is served at 160◦F and placed in a
room with an ambient temperature 75◦. After 5 minutes, the cup of
coffee has a temperature of 131◦F.
a) Create a...

A coffee-cup calorimeter initially contains 125 g water at 24.2
degrees celsius. Ammonium Nitrate (10.5 g), also at 24.2 degree
celsius, is added to the water, and after the ammonium nitrate
dissolves, the final temperature is 18.3 degrees celsius.What is
the heat of solution of ammonium nitrate in kj/mol? Assume that the
specific heat capacity of the solution is 4.18 J/Cg and that no
heat is transferred to the surrounds or to the calorimeter.

A 210 degree cup of coffee is placed on a table in a
climate-controlled room with the temperature set at a constant 73
degrees. After 6 minutes, the temperature of the coffee had dropped
to 150 degrees. Find a function that outputs the temperature of the
coffee t minutes after it is placed on the table.

A covered mug of coffee originally at 190 degrees Fahrenheit, if
left for t hours in a room whose temperature is 60
degrees, will cool to a temperature of
60 +
130e−1.7t
degrees. Find the temperature of the coffee after the following
amounts of time. (Round your answers to the nearest degree.)
(a) 15 minutes
°F
(b) half an hour
°F

The temperature, T, of a cup of tea is modelled by the
function T = 21 + 58.8(1.4)-x ,where T is measured in 0C (degrees
Celsius) and x is measured in minutes. The time starts to be
measured when the tea is poured into the cup.
1) Graph the function using
technology. Include a graph in your response.
2) Find the temperature of the tea in the cup in 0C
and 0F:
a) when the tea is poured into...

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