Question

A body is allowed to cool. It takes 15 minutes to
cool from 80°C to 60°C. The temperature of body
in next 15 minutes would be (temperature of
surrounding is 20°C)
(1) 41.6°C
(2) 46.7°C
(3) 49.2°C
(4) 52°C​

Answer 1

A body is allowed to cool. It takes 15 minutes to

cool from 80°C to 60°C. The temperature of body

in next 15 minutes would be  46.7 ° C

let the temperature of the body be Ф

t = time

by newtons law of cooling

 d Ф/dt = -k (Ф - Фa)

Фa = temperature of air

d Ф/(Ф - Фa) = -kdt

on integration  we get

Ф = Фa + Ze('-Kt)

here Фa = 20°C

so for t = 0 Ф = 80°C

Z = 60

now t = 15 Ф = 60° C

k = (1/15) ln (3/2)

now again at t = 30 min

Ф = 46.7 °C