The initial temperature of a body is 80 degree celcius If its temperature falls to 64 degree celcius in 5 min and in 10 min to 52 degree celcius then the temperature of surrounding will be

Dear pallavi

assume newtons law of cooling

dT/dt =-k(T-To)  ...................1

To is the temperature of sorrunding

dT = 64-80 =-16   

so dT/dt  =-16/5  ^oC /min

mean temperature T = (80 + 64)/2 = 72

so put these value in equation 1

-16/5 = -k(72 -To)   ....................a

for the next 5 sec

mean temperature T = (64 + 52)/2 =58

and dT/dt = (52-64)/5 = -12/5

so put again in equation  1

-12/5  = -k( 58 - To) ............b

now  divide equation a by b

 16/12   = (72-To) /(58-To)

To =16

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