00:01
In this question, we are given at 1 pm the thermometer reads 10 degree fahrenheit and it is removed from freezer and placed in a room where it reads after room temperature this is going to be 65 degree fahrenheit.
00:26
So next at 1 5 pm the thermometer reads 25 degree fahrenheit.
00:34
Later again the thermometer is placed inside the freezer.
00:38
So after at 1 30 pm the thermometer reads 32 degree fahrenheit.
00:47
When when was thermometer returned to the freezer and what was the thermometer reading at the time? so we have to find at what time thermometer is kept in the freezer.
01:09
So the one thing we have to find here is time the other one is the reading at that time when the thermometer is placed in the freezer.
01:21
So we have to use newton's law of cooling right here.
01:25
So let's recall the general form which states that dq over dt is equals to k times of ta subtracted by t.
01:37
So here the temperature of its surrounding as well as the temperature of the freezer.
01:43
So the q here is heat, k is constant, t is the temperature and ta is going to be the temperature of the room.
02:01
So as let's say q is equals to ct.
02:06
So the equation is formed as dt over dt is equals to ks ta subtracted by t.
02:18
So let's keep this as equation 1 and this as equation 2.
02:25
So let's solve this for only for dt.
02:29
So this is going to be dt over ta subtracted by t is equals to ks multiplied by dt.
02:40
So the solution for this equation as it takes a long time to evaluate.
02:44
I write it as d of t is equals to ta plus t not subtracted by ta e raised to the power of negative k not t.
02:56
So let's keep this as equation 3.
02:59
So here this t t of t not is that the t not is the initial temperature.
03:05
So this is going to be initial temperature.
03:10
So let's move forward and substitute the values we have.
03:15
So we have ta that is the thermometer temperature is 65 degree fahrenheit, t not that is the initial it is 10 degree fahrenheit and t of 300 which is going to be 25 degree fahrenheit.
03:34
This is in the terms of minutes.
03:36
So let's substitute the values.
03:42
So we'll be having t of t is as 25 is equals to t is 65 plus t not 10 subtracted by t a which is 65 e raised to the power of negative k not multiplied by...