= Cooling rate, T= Body's temperature, T0= Surrounding temperature and b= Constant. ∴ From Eq. (i),
∫
i
T
T
dT
T−T0
=−b
t
∫
0
dt ⇒T=T0+(Ti−T0)e−bt⋅⋅⋅⋅⋅⋅⋅(ii) From the first condition of question, T=40∘C T0=10∘C Ti=100∘C t=10min Putting these value in Eq. (ii), 40=10+(100−10)e−b×10 ⇒
30
90
=e−10b ⇒
1
3
=e−10b ⇒ln(
1
3
)=−10blnm ⇒ln1−ln3=−10b ⇒−ln3=−10b ⇒b=
ln3
10
=
1.1
10
Now, by next condition of question, T=20∘C Ti=70∘C Ta=10∘C From Eq. (ii), 20=10+(70−10)e−bt