How Does Newton's Law of Cooling Predict Time for Temperature Changes?

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SUMMARY

Newton's Law of Cooling predicts the rate of temperature change of an object in relation to the ambient temperature. In the discussion, a container of hot water at 80°C cools to 79°C in 15 seconds in a room at 20°C. Using this data, the time required for the water to cool from 70°C to 69°C and from 30°C to 29°C can be estimated using the formula derived from Newton's Law of Cooling. The initial calculation of 18.75 seconds was identified as incorrect, emphasizing the need for accurate application of the law.

PREREQUISITES
  • Understanding of Newton's Law of Cooling
  • Basic knowledge of temperature measurement
  • Ability to perform exponential decay calculations
  • Familiarity with differential equations
NEXT STEPS
  • Study the derivation of Newton's Law of Cooling
  • Practice solving temperature change problems using the law
  • Explore applications of Newton's Law of Cooling in real-world scenarios
  • Learn about the impact of varying ambient temperatures on cooling rates
USEFUL FOR

Students studying physics, particularly those focusing on thermodynamics, as well as educators and anyone interested in the practical applications of cooling laws in science and engineering.

dymand68
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Homework Statement


A container of hot water at 80°C cools to 79°C in 15 seconds when it is placed in a room that is at 20°C. Use Newton's law of cooling to estimate the time it will take for the container to cool from 70°C to 69°C.
And still later, from 30°C to 29°C.



Homework Equations


rate~change in temp.



The Attempt at a Solution


15*1.125=18.75 (incorrect)
 
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Look after Newton's law of cooling.

ehild
 

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