anonymous
  • anonymous
When an object is removed from a furnace and placed in an environment with a constant temperature of 90 degrees Fahrenheit , its core temperature is 1120 degrees Fahrenheit . Find the core temperature 5 hours after the object is removed from the furnace.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
This should be an application of Newton's Law of Cooling. The law says that the rate of change in the temperature of the object is proportional to the difference between the object temperature and the environment; that is,\[\frac{dT}{dt}=-k(T-T_{\infty})\]where k is positive, T is the object temperature and T_{infinity} that of the environment. This is a separable equation and you have\[\frac{dT}{T-T_{\infty}}=-kdt \rightarrow \log(T-T_{\infty})=-kt+c\]Exponentiating both sides gives,\[T-T_{\infty}=Ce^{-kt} \rightarrow T= Ce^{-kt}+T_{\infty}\]At t=0, the temperature of the object is its initial temperature, and so,\[T(0)=C+T_{\infty} \rightarrow C=T(0)-T_{\infty}\]Your equation is then\[T(t)=[T(0)-T_{\infty}]e^{-kt}+T_{\infty}\]Now, the problem you have here is that there isn't enough information to extract a numerical answer. We need some more info. to find k. From what you do have,\[T(t)=(1120-90)^oFe^{-kt}+90^oF\]\[=(1030^oF)e^{-kt}+90^oF\]At t=5 hours,\[T(5)=(1030^oF)e^{-5k}+90^oF\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.