A body takes 10 minutes to cool from 60oC to 50oC. The temperature of surroundings is constant at 25oC. Then, the temperature of the body after next 10 minutes will be approximately 43oC, 41oC, 47oC, or 45oC?

−dT/dt=k(T−T₀)
dT/(T−T₀)=−kdt
T=Temp of body
T₀=Temp. of surrounding=25oC
t=10min=10(60)=600sec
∫⁶⁰₅₀dT/(T−T₀)=−k[t]⁶⁰⁰₀
2.303k logₑ[T−T₀]⁶⁰₅₀=−k[600]
⇒2.303k logₑ[(60−25)/(50−25)]=600
⇒2.303k logₑ[35/25]=600 .. (1)
Now suppose for next 10 min, temp falls from 50 to T
2.303k logₑ[T−T₀]⁵⁰T=600
2.303k logₑ[(50−25)/(T−25)]=600 .. (2)
from (1) (2)
logₑ(35/25)=logₑ(25/(T−25))
35/25=25/(T−25)
35(T−25)=25²
35T−875=625
35T=1500
T=1500/35≈43oC