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A metal ball is heated to a temperature of 100∘C at time t=0, then placed in water which is maintained at 40∘C. If the temperature of the ball is reduced to 60∘C in 4 minutes, find the time at which the temperature of the ball is 50∘C. Given data: Rate of change of temperature of the body is given as dTdt=−k(T−Ts) where, T = Temperature of the body, Ts = Temperature of the surrounding, k = proportionality constant, t = time in minutes

Answer» A metal ball is heated to a temperature of 100C at time t=0, then placed in water which is maintained at 40C. If the temperature of the ball is reduced to 60C in 4 minutes, find the time at which the temperature of the ball is 50C.
Given data:
Rate of change of temperature of the body is given as
dTdt=k(TTs)
where, T = Temperature of the body,
Ts = Temperature of the surrounding,
k = proportionality constant,
t = time in minutes


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