{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

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 : t T T dt dT i i + ) ( 1 . Therefore t T T k T T T T k t T T a i i i a i i i + + ) ( ) ( ) ( 1 1 See attached Excel file for the implementation

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

View Full Document
PROBLEM 2 Determine the number of terms needed to approximate x cos to 8 significant figures. For x=0.3 π . Use .... ! 8 ! 6 ! 4 2 1 cos 8 6 4 2 + + = x x x x x ANSWER: 4444132198 . 0 2 ) 3 . 0 ( 2 2 2 = = π x 555867802 . 0 2 1 cos 2 = = x x 032875568
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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
Ask a homework question - tutors are online