Respuesta :
Answer:
Explanation:
Writing out the Newton's Law pf Cooling:
dT/dt = -k * (T - A),
where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.
If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C,
T = 100
A = 25
dT = 100 - 90 = 10
dt = 1
Putting the figures into the equation:
10/1 = -k * (100 - 25)
k = -10/75°C
After 4 minutes, dT/4 = 10/75 (100 - 25) = 10
dT = 40
Temperature after 4 minutes = 100 - 40 = 60°C
We can solve it mathematically also in simple way.
- Common difference=100-90=-10°C=d
- Initial=a=100
[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]
[tex]\\ \rm\Rrightarrow a_5=100+4(-10)[/tex]
[tex]\\ \rm\Rrightarrow a_5=100-40[/tex]
[tex]\\ \rm\Rrightarrow a_5=60°C[/tex]
