Explanation:
Given that,
Rate of cooling of air
Initial temperature= 80°C
Final temperature = 5°C
We need to calculate
Using newton's law of cooling
[tex]\dfrac{dT}{dt}=c(T-T_{0})[/tex]
[tex]\dfrac{dT}{dt}=c(\dfrac{T_{1}+T_{2}}{2}-T_{0})[/tex]
Where, [tex]dT=T_{1}-T_{2}[/tex]
Here, [tex]T =\dfrac{T_{1}+T_{2}}{2}[/tex]
[tex]T_{0}[/tex] = 25°C (surrounding temperature)
dt = 1 minute
[tex]\dfrac{dT}{dt}=c(\dfrac{T_{1}+T_{2}}{2}-T_{0})[/tex]
Put the value into the formula
[tex]\dfrac{80-5}{1}=c(\dfrac{85}{2}-25)[/tex]
[tex]c=\dfrac{75}{17.5}[/tex]
[tex]c=4.285\ cubic\ meter/minute[/tex]
Hence, This is the required answer.
