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]
3 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]3 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
The figure below is a regular octagon with a side length of 8 inches.
Masteriza [31]

Answer:

309in²

Step-by-step explanation:

Area of an octagon is expressed as;

A=2(1+√2)a²

a is the side length of the octagon

Given

a = 8

Substitute into the formula

A = 2(1+√2)(8)²

A = 2(1+√2)(64)

Expand

A = 2(64+64√2)

A = 128+128√2

A = 128+128(1.414)

A = 128+181.01

A = 309in²

Hence the area of the octagon is 309in²

3 0
3 years ago
456.4+678.345+56732+45.67+2222
denpristay [2]
60134.416 hope it helps
3 0
3 years ago
Read 2 more answers
Find the quotient. -105/15=
Salsk061 [2.6K]

Answer:

-7

Step-by-step explanation:

Hope this helped! :)

5 0
3 years ago
Read 2 more answers
20 miles<br> 1 gallon<br> 180 miles<br> gallons<br> What the answer
zlopas [31]

Answer:I dont know

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Match the vocabulary word with its definition
topjm [15]
Where is the picture? i cant see it
5 0
3 years ago
Read 2 more answers
Other questions:
  • Which has a larger value: 4 x 10^2 or 7 x 10^4?
    12·2 answers
  • For which pair of triangles would you use AAS to prove the congruence of the 2 triangles
    6·2 answers
  • You pull a Queen (any of 4 suits) out of 52-card deck. I pull a pair of grey socks from the 12 -pair pack. There are 3 pairs of
    11·1 answer
  • 3x + 10 &gt;28 inequality
    5·2 answers
  • 3. A basket of beads contains 8 red beads, 6 yellow beads, and 6 green beads. A
    11·1 answer
  • According to exponent rules, when we multiply the expressions we __ the exponents
    14·1 answer
  • Mr. Harris has batteries for his calculators. If b represents the number of batteries and c represents his calculators, how many
    5·1 answer
  • 1 1/5 divided by /10
    15·2 answers
  • Please help me im having trouble but my teacher wont give out awnsers
    12·2 answers
  • Find the length of x. Assume the triangles are similar.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!