PLS HELP ME what is the equation I really need it
1 answer:
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Answer:
A) cooling constant = 0.0101365
B)
c) F(t) = 60 + 77.46
D)137.46 ⁰
Step-by-step explanation:
water temperature = 60⁰F
temperature of Bar after 20 seconds = 120⁰F
temperature of Bar after 60 seconds = 100⁰F
A) Determine the cooling constant K
The newton's law of cooling is given as
=
= ∫ = ∫ k(60 - F)
= ∫ = ∫ kdt
= In (60 -F) = -kt - c
60 - F =
60 - F = ( note :
is a constant )
after 20 seconds
= 60 - 120 = -60
therefore ------- equation 1
after 60 seconds
= 60 - 100 = - 40
therefore -------- equation 2
solve equation 1 and equation 2 simultaneously
= =
= 6 = 4
= = In(6/4) = 40k
cooling constant (k) = In(6/4) / 40 = 0.40546 / 40 = 0.0101365
B) what is the differential equation satisfied
substituting the value of k into the newtons law of cooling)
60 - F =
F(t) = 60 -
The differential equation that the temperature F(t) of the bar
C) The formula for F(t)
t = 20 , F = 120
F(t ) = 60 -
120 = 60 -
= 60
= 77.46
C1 = - 77.46⁰ as the temperature is decreasing
The formula for f(t)
= F(t) = 60 + 77.46
D) Temperature of the bar at the moment it is submerged
F(0) = 60 + 77.46
F(0) = 60 + 77.46(1)
= 137.46⁰