1. What is Newton's Law of Cooling?

Newton's Law of Cooling states that the rate of heat loss of a body is directly proportional to the difference in temperatures between the body and its surroundings. It describes how the temperature of an object changes over time as it approaches the ambient temperature.

2. How Does the Calculator Work?

The calculator uses Newton's Law of Cooling equation:

Where:

• \( T \) — Final temperature (°C)
• \( T_a \) — Ambient temperature (°C)
• \( T_0 \) — Initial temperature (°C)
• \( k \) — Cooling constant (1/s)
• \( t \) — Time (s)

Explanation: The equation shows exponential decay of temperature difference between the object and its surroundings.

3. Derivation from Energy Balance

From energy balance: \( m c \frac{dT}{dt} = -h A (T - T_a) \)

Where:

• \( m \) — Mass of the object (kg)
• \( c \) — Specific heat capacity (J/kg·K)
• \( h \) — Heat transfer coefficient (W/m²K)
• \( A \) — Surface area (m²)

Derivation: Rearranging gives \( \frac{dT}{dt} = -\frac{h A}{m c} (T - T_a) \), where \( k = \frac{h A}{m c} \)

Final form: \( \frac{dT}{dt} = -k (T - T_a) \)

4. Using the Calculator

Tips: Enter initial temperature, ambient temperature, cooling constant, and time. All values must be valid (cooling constant > 0, time ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the cooling constant (k)?
A: The cooling constant represents how quickly an object cools. It depends on material properties, surface area, and heat transfer conditions.

Q2: When is Newton's Law of Cooling applicable?
A: It applies when the temperature difference is small, heat transfer is primarily by convection, and the object's temperature is uniform.

Q3: How do I determine the cooling constant experimentally?
A: Measure temperature at different times and use logarithmic analysis of the temperature difference vs. time plot.

Q4: What are the limitations of this law?
A: It assumes constant ambient temperature, negligible radiation heat transfer, and uniform temperature throughout the object.

Q5: Can this be used for heating processes?
A: Yes, the same equation applies when an object is heating up toward a warmer ambient temperature.