sir isaac newton question no.3 question 'n' answer
Answers
Explanation:
Question:
A hot metal bar is submerged in a large reservoir of water whose temperature is
55
o
F
. The temperature of the bar
20
s
after submersion is
95
o
F
. After
1
m
i
n
submerged, the temperature has cooled to
75
o
F
.
(a) Determine the cooling constant
k
.
(b) What is the differential equation satisfied by the temperature
F
(
t
)
of the bar?
(c) What is the formula for
F
(
t
)
?
(d) Determine the temperature of the bar at the moment it is submerged.
Newton's law of cooling:
Newton's law of cooling states that the rate of heat transfer between a body and its surrounding is directly proportional to the difference in their temperatures. It was in 1701 when Newton postulated the above statement, although at that time he did not write his law in the form of the differential equation we have today.
Answer and Explanation:
The following is an application of Newton's law of cooling. The Newton's law of cooling is given by the equation,
F
(
t
)
=
F
s
+
(
F
0
−
F
s
)
e
−
k
t
where
F
(
t
)
is the temperature at any given time
t
measured in seconds,
F
s
is the surrounding temperature, and
F
0
is the initial body temperature where all the temperature is measured in
∘
F
.
The variable
k
is the cooling rate and has the units
s
−
1
.
(a)
The value that we don't know is both the initial body temperature
F
0
and rate of cooling
k
.
Since, we are given with two points, we could rewrite the equation to cancel out
F
0
.
Explanation:
Question:
A hot metal bar is submerged in a large reservoir of water whose temperature is
55
o
F
. The temperature of the bar
20
s
after submersion is
95
o
F
. After
1
m
i
n
submerged, the temperature has cooled to
75
o
F
.
(a) Determine the cooling constant
k
.
(b) What is the differential equation satisfied by the temperature
F
(
t
)
of the bar?
(c) What is the formula for
F
(
t
)
?
(d) Determine the temperature of the bar at the moment it is submerged.
Newton's law of cooling:
Newton's law of cooling states that the rate of heat transfer between a body and its surrounding is directly proportional to the difference in their temperatures. It was in 1701 when Newton postulated the above statement, although at that time he did not write his law in the form of the differential equation we have today.
Answer and Explanation:
The following is an application of Newton's law of cooling. The Newton's law of cooling is given by the equation,
F
(
t
)
=
F
s
+
(
F
0
−
F
s
)
e
−
k
t
where
F
(
t
)
is the temperature at any given time
t
measured in seconds,
F
s
is the surrounding temperature, and
F
0
is the initial body temperature where all the temperature is measured in
∘
F
.
The variable
k
is the cooling rate and has the units
s
−
1
.
(a)
The value that we don't know is both the initial body temperature
F
0
and rate of cooling
k
.
Since, we are given with two points, we could rewrite the equation to cancel out
F
0
.