Understanding Newton's Law of Cooling: Definition, Equation, and Application

Click For Summary
SUMMARY

Newton's Law of Cooling is mathematically defined as dT/dt = k(T(t) - Ta), where T(t) is the temperature of the object and Ta is the ambient temperature. The constant k represents the cooling rate and is typically negative, indicating heat loss. The discussion highlights a common confusion regarding the placement of T(t) and Ta in the equation, emphasizing that the conventional form accurately reflects the physical process of heat transfer. The equation's structure is essential for understanding the dynamics of temperature change in relation to ambient conditions.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with thermodynamics concepts
  • Knowledge of temperature measurement and units
  • Basic grasp of mathematical modeling
NEXT STEPS
  • Study the implications of the cooling constant k in various materials
  • Explore real-world applications of Newton's Law of Cooling in forensic science
  • Learn about the derivation of Newton's Law of Cooling from first principles
  • Investigate alternative cooling models and their equations
USEFUL FOR

Students of physics, engineers involved in thermal analysis, and professionals in fields requiring temperature regulation will benefit from this discussion.

Arcthor
Messages
34
Reaction score
1
If the temperature of an object with temperature T(t) is place in a room with the ambient temperature Ta, Newtons Law of Cooling is defined as dT / dt = k (T(t) - Ta), correct?

This implies we would need a negative k-value. Wouldn't the equation therefore be described better if T(t) and Ta changed place? As in: dT / dt = k (Ta - T(t))

What am I missing?
 
Physics news on Phys.org
The convention is somewhat arbitrary, but I think it makes sense for heat loss to be negative and heat gain to be positive.
 
The firm of the equation I am familiar with is the one that you suggested.

Chet
 

Similar threads

Undergrad Newton's law of cooling - formula for constant k
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Extending Newton's laws -- Is the concept of force still defined?
  • · Replies 35 ·
2
Replies
35
Views
5K
Insights How to Apply Newton’s Second Law to Variable Mass Systems
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad The Feynman way of explaining Symmetry in Physical laws
  • · Replies 45 ·
2
Replies
45
Views
4K
Undergrad Question about Newton's Law of Cooling
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Newton's Law of Cooling - "k" constant
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Physics behind carryover cooking
  • · Replies 22 ·
Replies
22
Views
11K
Undergrad 1st law of Newton as a special case of the 2nd law (historical aspect)
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Understanding Newton's Law of Cooling and Its Derivation | dQ/dt = KA(dT/dx)"
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Non-Newtonian description of an accelerated object
  • · Replies 8 ·
Replies
8
Views
2K