Answer:
The temperature of coffee becomes 163.08 Fahrenheit.
Step-by-step explanation:
The Newton's law of cooling can be mathematically written as
[tex]-\frac{dT}{dt}=k(T-T_{room})\\\\\frac{-dT}{(T-T_{room})}=kdt[/tex]
Applying the limits in the above relation as
At t = 0 ; T= 200 F
At t =10 ; T = 180 F
[tex]-\int_{200}^{180}\frac{dT}{T-70}=\int_{0}^{10}kdt\\\\-ln(T-70)_{200}^{180}=k\times 10\\\\\therefore k=\frac{ln(1.181)}{10}\\\\\therefore k=0.0167[/tex]
Applying the limits in the above relation as
At t = 10 ; T= 180 F
At t =20 ; T = T F
[tex]-\int_{180}^{T}\frac{dT}{T-70}=\int_{10}^{20}0.0167dt\\\\-ln(T-70)_{180}^{T}=0.167\\\\\therefore T = 163.08F[/tex]
Answer:
The temperature of coffee becomes 163.08 Fahrenheit.
Step-by-step explanation:
