Question

You have taken a job as a production engineer at the Acme Candy Company. On your first day you are presented with a problem to solve. After candy bars are coated with chocolate, they continue down a conveyor to be wrapped. There has been a quality problem because a significant number of the bars are too hot when they are packaged. This results in partial melting of the wrappers due to the heat of the bar. Marketing has expressed concern because candy bars wrapped in inferior packaging will not sell due to customer concerns about tampering.

You are presented with data from a large sample (100 bars) taken from the line where the cooling rate was monitored. The bars are coated with chocolate at 175.69o Fahrenheit. This temperature assures even coating of the bars and cannot be changed. The plant is maintained at a constant temperature. Your problem is to determine the cooling rate for the bars so that the conveyor speed can be adjusted accordingly. Having just completed your upper level thermodynamics course, you know that the rate will be in the general form of Newton’s cooling law,

T=Be^-kt

where T is the temperature of the bar, B is a constant and k is the exponential cooling constant. You must determine this rate from a linearization of the data so that further statistical studies (which are much easier in a linear form) can be completed. To begin this project, linearize the data in and produce values for B and k.

Time seconds Temp (F)

0 175.69

1 173.5

2 171.21