Question

8) If an object is heated and then exposed to the air, it will lose heat at a rate which is proportional to the

instantaneous difference in temperature between the object and the air. The decay of the object

temperature back to the air temperature is given by: T=Toe^(-t/T)

Where To is the initial temperature elevation of the object and T is the elevation of the object temperature

at later times. The symbol “t” is the time after the heated object was exposed to the air and

“τ” is the characteristic time for the cooling. The characteristic time for cooling would depend on the mass of the

object, on its surface area, and on the wind speed.

If a branding iron is heated to 2000°C above the air temperature (20°C), and if τ=5min, what will its

temperature be 5, 10, and 15 minutes after it begins to cool?

Answer 1