Twenty minutes after being served a cup of fast-food coffee, it is still too hot

Question

Twenty minutes after being served a cup of fast-food coffee, it is still too hot to drink at 160digree F. Two minutes later, the temperature has dropped to 158 degree F. Your friend, whose coffee is also too hot to drink, speculates that since the temperature is dropping an average of 1 degree per minute, it was served at 180 degree F . Explain what is wrong with this line of reasoning about the coffee temperature. Find the actual serving temperature of the coffee, if the room temperature is 68 degree, if the room temperature is 68 degree F. Twenty minutes after being served a cup of fast-food coffee, it is still too hot to drink at 160 degree F. Two minutes later, the temperature has dropped to 158 degree F. Your friend, whose coffee is also too hot to drink, speculates that since the temperature is dropping an average of 1 degree per minute, it was served at 180 degree F . Explain what is wrong with this line of reasoning about the coffee temperature. Find the actual serving temperature of the coffee, if the room temperature is 68 degree, if the room temperature is 68 degree F.

Explanation / Answer

The decrease in temperature is not linear with respect to time because the time taken to decrease the temperature depends on difference between the temperature of coffee and surrounding temperature which are not same in both the cases. To decrease the temperature from 160 to 158 it takes 2 min Using newtons law of cooling dT1/t=k(T1-Ts) The temperature of coffee is 185.5 F I am 100% sure abt the answer

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