A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of the surroundings is 20 °C. | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-11 Thermal Properties of Matter



Q.22:- A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of the surroundings is 20 °C.

 

Answer:-

According to Newton’s law of cooling, we have

mc (T1 – T2)/t = k [(T1 + T2)/2   –  T0)]        —————(1)



mc/k  =   [(T1 + T2)/2   –  T0)]/[(T1 – T2)/t]

mc/k =  [(80+50)/2   –  20)]/[(80 – 50)/5]
= 45/6

Substituting T1 = 60 and T2 = 30 and T0 = 20  (all in °C) in Eq. (1), we get

mc (60 – 30)/t = k [(60+ 30)/2   –  20)]
30 mc/t  = 25 k
t = 30 mc/(25k)
= (30/25) x (45/6)
= 9 min

The body takes 9 min to cool from 60°C to 30 °C.