00:01
In this question, we have been given that initial temperature of a thermometer reading is 70 degree fahrenheit and the room temperature is given to be 10.
00:11
So let's say it is tr which is given as 10.
00:14
It says that after 5 minutes, the temperature becomes 40.
00:24
We have to find the time when the temperature is 20.
00:27
T.
00:28
Okay.
00:28
So use newton's law of cooling for this.
00:33
Newton's law of cooling according to which we get t of t equals to the room temperature plus initial minus the room temperature e raised to minus k times of t correct where k is a constant t is time correct so here we have after 5 minute if we consider after 5 minute what happens temperature becomes 40 room temperature is 10 plus initial was 70 minus 10 e raised to minus t is 5 so so here we get minus 5k.
01:17
So this comes out to be 30 equals to 60 e raised to minus 5k.
01:23
E raised to minus 5k is half.
01:26
Take log minus 5k equals to log of half.
01:30
This implies k is equals to minus 1 over 5 log of half.
01:37
So we are getting value of k equals to 0 .138629...