Newton's law of cooling states that a body at temperature T(t) will cool down to an...

 

Transcribed Image Text:

Newton's law of cooling states that a body at temperature T(t) will cool down to an ambient temper- ature of Ta (t) at constant rate, such that dT dt = = X(Ta - T), where is a constant with units of inverse seconds. Use this physical law to solve the following, real- world problem. You buy a coffee in Tim Hortons, where the ambient temperature is Ta 25C, and measure its temperature to be To 77C using a thermometer. After T = 100 seconds of using the local free WiFi, and neglecting to drink your coffee, you notice that the temperature is now T = 70C. At that moment, you suddenly realize the time, rush through the door outside, and head to your lecture, where you wait outside LSK to offer the professor some chocolate before the lecture begins. It is now six minutes after buying the coffee, and you take the first sip. (a) (2 pts) Find the value of from the temperature measurements inside the Tim Hortons. Predict the temperature of the coffee when you first take a sip, if the outdoor temperature is (due to catastrophic global warming). (b) (1 pts) Ta = 15C, (c) (2 pts) Ta = T(1 + at), with a = 0.0038462sec and T = 10C. Drinking a liquid over about 60C will cause burns instantaneously; it will still be too hot to drink comfortably if over about 44C. Are you happy, uncomfortable or burnt in (b) and (c)? (1 pt) Newton's law of cooling states that a body at temperature T(t) will cool down to an ambient temper- ature of Ta (t) at constant rate, such that dT dt = = X(Ta - T), where is a constant with units of inverse seconds. Use this physical law to solve the following, real- world problem. You buy a coffee in Tim Hortons, where the ambient temperature is Ta 25C, and measure its temperature to be To 77C using a thermometer. After T = 100 seconds of using the local free WiFi, and neglecting to drink your coffee, you notice that the temperature is now T = 70C. At that moment, you suddenly realize the time, rush through the door outside, and head to your lecture, where you wait outside LSK to offer the professor some chocolate before the lecture begins. It is now six minutes after buying the coffee, and you take the first sip. (a) (2 pts) Find the value of from the temperature measurements inside the Tim Hortons. Predict the temperature of the coffee when you first take a sip, if the outdoor temperature is (due to catastrophic global warming). (b) (1 pts) Ta = 15C, (c) (2 pts) Ta = T(1 + at), with a = 0.0038462sec and T = 10C. Drinking a liquid over about 60C will cause burns instantaneously; it will still be too hot to drink comfortably if over about 44C. Are you happy, uncomfortable or burnt in (b) and (c)? (1 pt)