10 A thermometțer showing 10°C js brought into a room whose femperature is 27°C After 5 mīnutes , it shows 20°C - when will the thermometer practically feach the temperature 26°C 7

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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li
No:..
Subject.
Date:
NEWTON'S LAW OF COOLING: SOLVING THE DIFFERENTIAL EQUAT) ONS
First order inifial value problem:
di = -k (T-Ts), I (0) = To,
dt
%3D
%3D
2-separate vatiables :
dT
ード dt
T-Ts
3- Integrate both sides of equation:
nIT-Ts '
e
-kナtC
:e
dt
-kt.e
T-Ts
T-ts = e
T=4ekt
tTe
In |T -Ts | = -kt † C
4 Apply the properties of natural logatīthms and simplifying :
-kt
T = Ts t Ae ". A = e°
C
No .
Subject:.
Date:
10.A thermomefer showing 10°C je broyght ibto a toom whose femperature is
27°C· After 5 Mīnutes , if shows 20°C - when will the thermometer
practically Feach the temperature 26°C 7 .
Transcribed Image Text:li No:.. Subject. Date: NEWTON'S LAW OF COOLING: SOLVING THE DIFFERENTIAL EQUAT) ONS First order inifial value problem: di = -k (T-Ts), I (0) = To, dt %3D %3D 2-separate vatiables : dT ード dt T-Ts 3- Integrate both sides of equation: nIT-Ts ' e -kナtC :e dt -kt.e T-Ts T-ts = e T=4ekt tTe In |T -Ts | = -kt † C 4 Apply the properties of natural logatīthms and simplifying : -kt T = Ts t Ae ". A = e° C No . Subject:. Date: 10.A thermomefer showing 10°C je broyght ibto a toom whose femperature is 27°C· After 5 Mīnutes , if shows 20°C - when will the thermometer practically Feach the temperature 26°C 7 .
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