Question

if a body cools from 80 degree to 50 degree at room temperature of 25 degree Celsius in 30 minutes find the temperature of body after 1 hour​

Answer 1

Answer:

body cool from 110 degree to 80 degree at room temperature of 40 degree Celsius in 1 hour

Answer 2

After one hour temperature of the body will be 36.33°C.

Step-by-step explanation:

By Newton's law of cooling,

$T_{t}=T_{i}+(T_{0}-T_{i})e^{kt}$

where

$T_{t}$= Temperature after time 't'

$T_{i}$ = temperature of environment

$T_{0}$ = Initial temperature of the object

k = constant

t = duration or time

Now we plug in the values given in the question to find the value of the constant.

$50=25+(80-25)e^{0.5k}$

$50-25=(80-25)e^{0.5k}$

$e^{0.5k}=\frac{25}{55}$

$e^{0.5k}=\frac{5}{11}$

$ln(e^{0.5k})=ln(\frac{5}{11} )$

0.5k = ln5 - ln11

0.5k = 1.6094 - 2.3979

k = -1.577 ≈ -1.58

Now the equation will be

$T_{t}=T_{i}+(T_{0}-T_{i})e^{-1.58t}$

Now t = 1 hour

$T_{t}=25+(80-25)e^{-1.58\times 1}$

$T_{t}=25+55e^{-1.58}$

$T_{t}$ = 36.33° C

Therefore, after one hour temperature of the body will be 36.33 °C.

Learn more about the Newton's law of cooling from :

brainly.in/question/1513680