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Newton's Law of Cooling Calculator
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Newton’s Law of Cooling can be define as “the rate of change of the temperature of an object is proportional to the difference in temperatures between the body and its surroundings.”
Newton's Law of Cooling Calculator will help to calculate the temperature of the object at time(t).
 

Steps for Newton's Law of Cooling Calculator

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Step 1 :  

Observe the value of surrounding constant temperature(Ts), Initial temperature of the object(To), core temperature(T) and time(t). 



Step 2 :  

Apply the formula:


Temperature of the object at time t, T (t) = Ts + (To - Ts)*e(-k*t)



Problems on Newton's Law of Cooling Calculator

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  1. Calculate law of cooling of the object for the given details

    Surrounding constant temperature (Ts) = 40
    Initial temperature of the object (To) = 20
    Core Temperature (T) = 30
    Time(t) = 22


    Step 1 :  

    Given that:


    Surrounding constant temperature (Ts) = 40
    Initial temperature of the object (To) = 20
    Core Temperature (T) = 30
    Time(t) = 22



    Step 2 :  

    Temperature of the object at time t, T (t) = Ts + (To - Ts)*e(-k*t)  


    k = log($\frac{(30-40)}{(20-40)}$) = -0.301029996


    T (t) = 40 + (20 - 40)*e(-0.301029996*22)  


    T (t) = 39.973 F



    Answer  :  

    T (t) = 39.973 F



  2. Calculate law of cooling of the object for the given details

    Surrounding constant temperature (Ts) = 50
    Initial temperature of the object (To) = 20
    Core Temperature (T) = 20
    Time(t) = 22


    Step 1 :  

    Given that:


    Surrounding constant temperature (Ts) = 50
    Initial temperature of the object (To) = 20
    Core Temperature (T) = 20
    Time(t) = 22



    Step 2 :  

    Temperature of the object at time t, T (t) = Ts + (To - Ts)*e(-k*t)  


    k = log($\frac{(20-50)}{(20-50)}$) = 0


    T (t) = 50 + (20 - 50)*e(-0*22)  = 50 + (-30) = 50 - 30 = 20


    T (t) = 20 F



    Answer  :  

    T (t) = 20 F



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