help me///// plz

Question

A certain object, after being heated, cools at such a rate that its temperture T(in  degree Celsius) decreases 20% in each minute. If the object is originally heated to 100 degrees Celsius, find limit (t  => 5) T and limit (t => infinity) T, where t is the time. (in min.)

 

limit (t =>5) T = ? degree Celsius.    

What's the answer is going to be....?

Answer 1

Given that object is originally heated to 100 degrees

Let us assume the local temparature or ambiance temperature  (Ta) is 30° Celsius

By using newton's law of cooling 

Where T is temperature of object

          t is time in minits

          Ta is ambiance temperature

Now separate the variables 

Integrate both sides 

Intially the object is heated to 100° ⇒T(0)=100

Given that Temperture T decreases 20% in each minute for 1st minit it decreases means 

T(1)= 100 - 20% of 100

T(1) = 100 -20 ⇒80

T(1) = 80

Now we have to calculate for limit (t  => 5)

So the temperature at time (t  => 5) is  >=43.046

Now we have to calculate for limit (t  => infinity)

So at infinite time the temperature of object is equal to temperature of ambiance = 30