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andyrk
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Newton's law of cooling is: dQ/dt = KA(θ - θo). Then where does the equation dQ/dt = KA(dT/dx) come from?
andyrk said:Newton's law of cooling is: dQ/dt = KA(θ - θo).
andyrk said:Then where does the equation dQ/dt = KA(dT/dx) come from?
How can dQ/dt have two different dimensions?Orodruin said:This generally applies to the surface interface between two materials.
This is Fourier's law (or something reminiscent of it, you really should define what you mean by Q). It applies to the heat transfer within a material.
Well, Fourier's law is actually just a statement on the current. What appears in the left hand side is the heat transfer per unit time across a surface. This can be related to an actual change in temperature (or heat, they are related by heat capacity, volume, and density) through the continuity equation.andyrk said:I would say that Q means different things too. Q in Newton's law of cooling is temperature whereas in Fourier's law it is heat.
Newton's Law of Cooling is a mathematical formula that describes the rate at which a hot object cools down in a cooler environment. It states that the rate of heat loss (dQ/dt) is directly proportional to the temperature difference between the object and its surroundings (ΔT), and is also proportional to the surface area (A) and the thermal conductivity (K) of the object.
The derivation of Newton's Law of Cooling involves using basic principles of heat transfer and calculus. It starts by assuming that the rate of heat loss is directly proportional to the temperature difference, and then using a small temperature difference ΔT to approximate the rate of change of temperature (dT/dt). This leads to the final formula dQ/dt = KA(dT/dx), where x is the distance from the surface of the object.
Newton's Law of Cooling has many practical applications, such as in determining the cooling rate of hot beverages, predicting the cooling of electronic devices, and understanding the cooling of the Earth's atmosphere. It is also used in industries that involve heat transfer, such as refrigeration and air conditioning.
The rate of cooling according to Newton's Law is affected by the temperature difference between the object and its surroundings, the surface area of the object, and the thermal conductivity of the object. Additionally, factors such as air flow, humidity, and insulation can also affect the cooling rate.
Newton's Law of Cooling is an application of the Second Law of Thermodynamics, which states that heat will always flow from a hotter object to a cooler object. It also demonstrates the concept of entropy, as the total amount of energy in a system tends to decrease over time, resulting in a decrease in temperature.