dT 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, K[M(t)- T(t)], where K is a constant. Let K=0.04 (min) and the temperature of the medium be constant, M(t) = 291 kelvins. If the body is initially at 365 kelvins, use Euler's method with h = 0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes. (a) The temperature of the body after 30 minutes is kelvins. (Round to two decimal places as needed.) C
dT 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, K[M(t)- T(t)], where K is a constant. Let K=0.04 (min) and the temperature of the medium be constant, M(t) = 291 kelvins. If the body is initially at 365 kelvins, use Euler's method with h = 0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes. (a) The temperature of the body after 30 minutes is kelvins. (Round to two decimal places as needed.) C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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find T_30 and T-60
![## 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. Mathematically, this is expressed as:
\[ \frac{dT}{dt} = K \left[ M(t) - T(t) \right] \]
where \( K \) is a constant.
In the given scenario:
- \( K = 0.04 \, (\text{min}^{-1}) \)
- The temperature of the medium is constant, \( M(t) = 291 \) kelvins
- The body is initially at 365 kelvins
Using Euler's method with a step size \( h = 0.1 \) min, approximate the temperature of the body after:
### (a) 30 minutes
The temperature of the body after 30 minutes is:
\[ \boxed{\phantom{0}} \text{kelvins}. \]
(Round to two decimal places as needed.)
### (b) 60 minutes
The temperature of the body after 60 minutes is:
\[ \boxed{\phantom{0}} \text{kelvins}. \]
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc45acf51-cefc-42df-83e4-535a253da58c%2F28eb6fee-fed1-48b4-8d8c-7d70dfa23497%2Ffkaugan_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## 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. Mathematically, this is expressed as:
\[ \frac{dT}{dt} = K \left[ M(t) - T(t) \right] \]
where \( K \) is a constant.
In the given scenario:
- \( K = 0.04 \, (\text{min}^{-1}) \)
- The temperature of the medium is constant, \( M(t) = 291 \) kelvins
- The body is initially at 365 kelvins
Using Euler's method with a step size \( h = 0.1 \) min, approximate the temperature of the body after:
### (a) 30 minutes
The temperature of the body after 30 minutes is:
\[ \boxed{\phantom{0}} \text{kelvins}. \]
(Round to two decimal places as needed.)
### (b) 60 minutes
The temperature of the body after 60 minutes is:
\[ \boxed{\phantom{0}} \text{kelvins}. \]
(Round to two decimal places as needed.)
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