Given,
In case 1 , body cools from temperature
70∘ to
40∘C i.e.
T1=70∘C,T2=40∘C and time
t1=5min In case 2 , temperature reduces from
60∘C to
40∘C in time
(t2) i.e,
T3=60∘C,T4=40∘C,t2= ?
Consider temperature of surrounding,
Ts=20∘C.
By using Newton's law of cooling,
‌=K(‌−Ts). . . (i)
where,
Ti,Tf be initial and final temperature of body,
t is the time taken by body to reach
Ti to
Tf and
K is thermal heat coefficient.
ccording to first case, By using Eq. (i), we get
‌‌‌‌=K(‌−Ts) ∴‌‌‌‌=K(‌−20) ⇒‌‌‌‌=K(‌−20)⇒6=K(35) ⇒‌K‌‌=‌ According to second case, again by using Eq. (i), we get
‌‌‌=K(‌−Ts) ‌‌‌=‌(‌−20) ⇒‌‌‌‌‌=‌×30⇒‌=‌×6 t2‌‌=‌=‌=3.89min