Question 42108
Let the rate of cooling = Q degrees/min., temperature of the plate = {{{T^o}}} C, temperature of surrounding air = {{{t^o}}} C.


According to given condition: 
{{{Q = k(T-t)}}} _________(1)
 where k = constant of variation.
When T = 270, t = 20, Q = 50.
Putting these values of T, t and Q in (1) we have
{{{50=k(270-20)}}}
or {{{k = 50/220}}} = {{{5/22}}}


Substituting this value of k in (1) we have
{{{Q = (5/22)(T-t)}}} _________(2)


When, T = 100 and t = 20 [assuming temperature of surrounding air remains constant] then from (2),
{{{Q = (5/22)(100-20)}}}
or {{{Q = (5/22)80}}} = {{{200/11}}} = 18.18 (approx)


Hence, reqd. rate of cooling is {{{18.18^o}}} per minute.