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.
