The initial temperature of a substance is 5°C. It is decreasing by 1°C after
5 minutes. What will its temperature be after 15 minutes?
Answers
Step-by-step explanation:
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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
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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
The temperature of a substance after 15 minutes is 2° C.
Given: The initial temperature of a substance is 5°C. It is decreasing by 1°C after 5 minutes.
To Find: The temperature of a substance after 15 minutes.
Solution:
It is said that the temperature decreases by 1° C after every 5 minutes.
The decrease in temperature every 5 min = 1° C
∴ the decrease in temperature every 1 min = (1 / 5 )° C
∴ the decrease in temperature in 15 min = (15 / 5 )° C
= 3° C
The initial temperature of the substance = 5° C
∴ temperature after 15 min = 5° C - 3° C
= 2° C
Hence, the temperature of a substance after 15 minutes is 2° C.
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