QUIZ-1-Answers - QUIZ #1 ENGR 3723 PROBLEM 1 Newtons law of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
QUIZ #1 ENGR 3723 PROBLEM 1 Newton’s law of cooling says that the temperature of a body ( T )changes at a rate that is proportional to the difference between its temperature and the surrounding medium (usually the ambient) ( T a ), that is: ) ( a T T k dt dT = where k is the heat transfer coefficient. a) Obtain the formula for temperature vs. time b) Integrate numerically and compare, for the temperature of a cup of coffee that is initially at 68 o C. (use k=0.017/min. You choose the value of T a ). What is the largest error incurred by the approximate formula? ANSWER: kt K T T kdt T T d kdt T T dT T T k dt dT a a a a = = = = ) ln( ) ln( ) ( ) ( But T=T 0 at t= 0 . Then K T T a = ) ln( 0 . Therefore: kt a a kt a a kt a a a a a a e T T T T e T T T T e T T T T kt T T T T kt T T T T + = = = = = ) ( ) ( ) ( ) ( ) ( ) ( ) ( ln ) ln( ) ln( 0 0 0 0 0 Therefore: kt a a e T T T T + = ) ( 0 Numerical integration :
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/31/2011 for the course ENGR 3723 taught by Professor Staff during the Summer '11 term at Oklahoma State.

Page1 / 2

QUIZ-1-Answers - QUIZ #1 ENGR 3723 PROBLEM 1 Newtons law of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online