Answer to Question #161881 in Mechanical Engineering for Sai preeth varma Lolakpuri

Question

A body kept in air with 25degree Celsius cools from 140 degree Celsius to 80 degree Celsius in 20 minutes. Find when body cools down to 35 degree Celsius.

Answer 1

According to Newton's law of cooling,

 mc

(T1 - T2)/t = k [(T1 +

T2)/2 - T0)]    ---------------(1) 

mc/k =  [(T1 +

T2)/2 - T0)]/[(T1 - T2)/t] mc/k

= [(140+80)/2 - 35)]/[(140 -

80)/25]    

  =

75/2.4

 

 Substituting

T1 = 140 and T2 = 80 and T0 = 25 (all in °C) in Eq. (1),

we

get mc (140 - 80)/t = k [(140+ 80)/2 - 25)]  80

mc/t

 =

25 k t

=

30 mc/(25k)   

=

(30/25) x (75/2.4) 

 =

37.5 min