1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aleks [24]
2 years ago
5

A pan of warm water (46∘ Celsius) was put in a refrigerator. After 15 minutes, the water's temperature was 27∘ C; 15 minutes aft

er that, it was 19∘C. Use Newton's Law of Cooling to determine how cold the refrigerator was.
Mathematics
1 answer:
Cloud [144]2 years ago
6 0

Answer:

The refrigerator was at around 13 ∘C

Step-by-step explanation:

Newton's Law of Cooling:

The rate of change of a body temperature  (amount of heat loss/time of loss) is directly proportional to the difference between its own temperature and the surroundings.

\frac{T(t2)-T(t1)}{t2-t1} = -h (T(t2) - Tenv)

T ⇒ temperature

t ⇒ time

Tenv ⇒refrigerator temperature

\frac{T(t2)-T(t1)}{t2-t1} ⇒ rate of change of he temperature

-h ⇒ constant of proportionality (negative because the temperature is decreasing inside the refrigerator)

We have 3 points:

time (minutes) - Temperature (∘ C)

0 (when the pan was put in the refrigerator) - 46

15 (after 15 minutes) - 27

30 (15 minutes after the first 15 minutes) - 19

\frac{27 - 46}{15 - 0} = -h (27 - Tenv)

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)

Now we have a system of two equations and two variables

\frac{-19}{15} = -h (27 - Tenv)\\ \frac{19}{15} = h (27 - Tenv)\\ \frac{19}{15(27 - Tenv)} = h

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)\\\frac{-8}{15} = -h (19 - Tenv)\\\frac{8}{15} = h (19 - Tenv)\\\frac{8}{15} = \frac{19}{15(27 - Tenv)} (19 - Tenv)\\8(27 - Tenv) = 19 (19 - Tenv)\\216 - 8 Tenv = 361 - 19 Tenv\\19 Tenv - 8 Tenv = 361 - 216\\11 Tenv = 145 \\Tenv = 145/ 11\\Tenv = 13. 18

The refrigerator was at around 13 ∘C

You might be interested in
A cat rescue service found homes for 40 cats in 5 weeks. What was the rate of cats being placed per week? Which ratio is equal t
ExtremeBDS [4]
A. 8 cats per week. if you simplify 40/5, it equals 8/1
7 0
3 years ago
Read 2 more answers
Find the coordinates of the midpoint of HX (SHOW YOUR WORK) H(0,0),X(8,4)
prisoha [69]
Y = mx + c
y = 0.5x
y = 0.5*4 = 2
(4,2)
7 0
3 years ago
HELP PLEASE
jok3333 [9.3K]

Answer:

b

Step-by-step explanation:

I mean I believe its b it looks like theres three

3 0
3 years ago
What is the image of (-5, 6) after a reflection over the line y = -2
prohojiy [21]

Answer:

I'm pretty sure it would be (5,6)

Step-by-step explanation:

Reflecting a point over the Y-axis would change the x-coordinate, but not the y-coordinate

6 0
3 years ago
EVALAUTE: 5|7 - 9| - 2=<br><br> a. -12<br> b. 0<br> c. 1<br> d. 8
alexandr1967 [171]
It’s d!!!!!!!!!!!!!!
3 0
3 years ago
Other questions:
  • Pedro cut a sheet of poster board into 10 equal parts. His brother used some of the poster board and now 8/10 is left. Pedro wan
    8·2 answers
  • Is x+y^3=27 a function?
    15·1 answer
  • 37.362 is 7 4/5 % of what number?
    6·1 answer
  • What is the factorization of 729^15+1000?
    5·1 answer
  • What is the range of the data below? A box-and-whisker plot. The number line goes from 100 to 125. The whiskers range from 102 t
    10·2 answers
  • Evaluate the expression |- 178|
    8·2 answers
  • Response will be saved automatically.
    7·1 answer
  • Jeffrey walked 1/2 Mile on Monday and jogged 2/3 Mile on Tuesday how far did he walk and jog on Monday And Tuesday combined
    15·2 answers
  • Which is a perfect square?<br> O 5<br> 0001<br> O<br> 36<br> 44
    15·1 answer
  • a gas company in massachusetts charges $1.30 for 16.7 ft3 of natural gas. convert this rate to dollars per liter of gas
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!