Rate Of Cooling Formula In Physics

Newton's Law of Cooling Extended Formula:

\[ \frac{dT}{dt} = -k A \frac{(T - T_a)}{m c} \]

Heat Transfer Coefficient (k):

W/m²K

Surface Area (A):

m²

Object Temperature (T):

°C

Ambient Temperature (T_a):

°C

Mass (m):

Specific Heat Capacity (c):

J/kgK

Rate of Cooling (dT/dt):

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1. What is Newton's Law of Cooling Extended?

Newton's Law of Cooling Extended describes the rate at which an object changes temperature through heat transfer. It extends the basic Newton's law by accounting for the object's mass and specific heat capacity, providing a more comprehensive model for temperature change over time.

2. How Does the Calculator Work?

The calculator uses the extended Newton's Law of Cooling formula:

\[ \frac{dT}{dt} = -k A \frac{(T - T_a)}{m c} \]

Where:

\( \frac{dT}{dt} \) — Rate of temperature change (°C/s)
\( k \) — Heat transfer coefficient (W/m²K)
\( A \) — Surface area (m²)
\( T \) — Object temperature (°C)
\( T_a \) — Ambient temperature (°C)
\( m \) — Mass of the object (kg)
\( c \) — Specific heat capacity (J/kgK)

Explanation: The negative sign indicates cooling when the object is hotter than the environment. The formula shows that cooling rate depends on temperature difference, surface area, heat transfer coefficient, and the object's thermal mass.

3. Importance of Rate of Cooling Calculation

Details: Understanding cooling rates is crucial in engineering applications like cooling systems design, material processing, food preservation, electronic device cooling, and thermal management in various industrial processes.

4. Using the Calculator

Tips: Enter all parameters in SI units. Ensure heat transfer coefficient, surface area, mass, and specific heat capacity are positive values. Temperature difference drives the cooling process.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between basic and extended Newton's Law?
A: The basic law assumes constant cooling rate per unit temperature difference, while the extended version accounts for object mass and specific heat capacity for more accurate predictions.

Q2: When is this formula most accurate?
A: This formula works best for forced convection scenarios with relatively small temperature differences and uniform temperature distribution within the object.

Q3: What affects the heat transfer coefficient (k)?
A: k depends on fluid properties, flow velocity, surface roughness, and temperature. It varies significantly between natural and forced convection scenarios.

Q4: Can this formula predict temperature over time?
A: Yes, by integrating the rate equation, you can predict temperature as a function of time: \( T(t) = T_a + (T_0 - T_a)e^{-kt} \).

Q5: What are typical values for specific heat capacity?
A: Water: ~4186 J/kgK, Aluminum: ~900 J/kgK, Steel: ~500 J/kgK, Copper: ~385 J/kgK. These values affect how quickly objects heat up or cool down.