A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of the surroundings is 20 °C.
Answers
Answered by
473
Here,
Initial temperature ( Ti) = 80°C
Final temperature ( Tf) = 50°C
Temperature of the surrounding ( To) = 20°C
t = 5 min
A/C to Newton's law of cooling
Rate of cooling ( dT/dt) = K[ (Ti+Tf)/2 - To]
( Tf - Ti)/t = K[ ( 80 + 50)/2 - 20]
( 80-50)/5 = K[ 65 - 20]
6 = K× 45
K = 6/45 = 2/15
in second condition,
initial temperature ( Ti) = 60°C
Final temperature ( Tf) = 30°C
Time taken for cooling is t
A/C Newton's law of cooling
( 60 - 30)/t = 2/15 [ (60+30)/2 -20]
30/t = 2/15 × 25
30/t = 50/15 = 10/3
t = 9 min
Answered by
0
Explanation:
dT
=−K(T−T
s
)+T
i
n
∴ Here from newtons law of co0ling
dt
dT
=−k(
2
T
f
+T
i
−T
s
)
∴
△t
T
f
−T
i
=K[
2
T
f
+T
i
−T
s
]
∴K=
20
1
⇒=
10
60−T
=
20
1
[
2
60+T
−30]
=120−2T=
21
T+60
−30
2
5T
=120
T=48
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