Newton's Law of Cooling Calculator
Calculate temperature changes over time using Newton's law of cooling formula
Newton's Law of Cooling Calculator
Material-dependent constant (typically 0.001 to 0.1 s⁻¹)
Cooling Results
Formula used: T = T∞ + (T₀ - T∞) × e^(-kt)
Parameters: T₀ = 100°, T∞ = 22°, k = 0.015000 s⁻¹
Time elapsed: 2.0 minutes
Cooling Analysis
Example Calculation
Coffee Cooling Example
Initial coffee temperature: 100°C
Room temperature: 22°C
Cooling coefficient: 0.015 s⁻¹
Time: 2 minutes (120 seconds)
Calculation
T = T∞ + (T₀ - T∞) × e^(-kt)
T = 22 + (100 - 22) × e^(-0.015 × 120)
T = 22 + 78 × e^(-1.8)
T = 22 + 78 × 0.165
T = 34.9°C
Heat Transfer Mechanisms
Conduction
Heat transfer through direct contact
Convection
Heat transfer by fluid motion
Radiation
Heat transfer by electromagnetic waves
Typical Cooling Coefficients
Physics Tips
Newton's law applies when the object temperature is uniform
Larger temperature differences lead to faster cooling
Cooling rate decreases exponentially over time
Ambient temperature acts as the cooling limit
Understanding Newton's Law of Cooling
What is Newton's Law of Cooling?
Newton's Law of Cooling states that the rate of change of temperature of an object is proportional to the difference between its own temperature and the ambient temperature. This law describes how objects cool down (or heat up) when placed in a different temperature environment.
Key Applications
- •Food and beverage cooling
- •Forensic science (time of death estimation)
- •HVAC system design
- •Industrial process cooling
Mathematical Formula
T = T∞ + (T₀ - T∞) × e^(-kt)
- T: Temperature at time t
- T∞: Ambient temperature (final temperature)
- T₀: Initial temperature
- k: Cooling coefficient (s⁻¹)
- t: Time elapsed
Note: The cooling coefficient k depends on the material properties, surface area, and heat transfer mechanism involved.
Cooling Coefficient Calculation
The cooling coefficient can be calculated from material properties using the formula:
k = hA/C
h - Heat Transfer Coefficient
Depends on the heat transfer mechanism (conduction, convection, radiation)
A - Surface Area
The area through which heat is being transferred
C - Heat Capacity
The amount of heat needed to raise temperature by 1 degree