An object is heated to 90 degrees Celcius and is then allowed to cool in a room whose air temperature is 25 degrees celcius. If the temperature of the object is 75 degrees celcius after 10 minutes, when will its temperature be 50 degrees celcius?

Answer 1

You will need Newton's Law of Cooling formula, which is
T(t) = T_m + (T₀ - T_m)e^(kt)

where T(t) is the current temperature of the object
T_m is the surrounding temperature and
T₀is the starting temperature
t is in minutes, and k is a constant

first we have to find the value of k

75 = 25 + (90-25)e^(10k)
50 = 65 e^(10k)
.76923 = e^(10k)
10k = ln .76923
k = -.026236

so now
50 = 25 + (90-25)e^(-.026236t)
25/65 = e^(-.026236t)
(-.026236t) = ln(25/65)
t = 36.42 minutes

Answer 2

Thank you!!!