contestada

A hot object cools down according to Newton's Law so that t hours after the start, the rate that heat leaves is 57????−????/3 Joules per hour. How much heat leaves the object during the first 7 hours? [All you need to know is that a Joule is a quantity of heat. In fact, 4.2 Joules is the heat required to raise 1 gram of water 1 degree Celcius]

Respuesta :

Answer:

H = 154.41 J

Explanation:

given,

rate at which heat leaves

[tex]\dfrac{dH}{dt}=57e^{-t/3}[/tex]

Heat leaves during first 7 hours

[tex]dH = 57e^{-t/3}dt[/tex]

integrating both side

[tex]\int dH =\int_0^7 57e^{-t/3}dt[/tex]

[tex]H = 57\dfrac{e^{-t/3}}{\dfrac{-1}{3}}[/tex]

[tex]H = -57\times 3 [e^{-t/3}]_0^7[/tex]

[tex]H = -171[e^{\dfrac{-7}{3}}-e^{0}][/tex]

H = 154.41 J

Hence,heat the object during the first 7 hours is equal to 154.41 J.

Otras preguntas