Thermodynamic temperature derivation

• kelvin490
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kelvin490

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In deriving thermodynamic temperature scale, it uses the concept that heat transfer between two reservoirs is the function of the reservoirs' temperatures. i.e. Q1/Q2=Φ(T1,T2). And then further express that Φ(T1,T2)=ψ(T1)/ψ(T2).

I have two questions, 1. Is it a hidden assumption that the function Φ doesn't change its form for different temperatures? i.e. for different reservoirs we just plug in different temperatures Φ(T1,T2), Φ(T3,T4) but it can never be some other functions for different temperatures. Why?

2. Why Φ(T1,T2) can be expressed as ψ(T1)/ψ(T2)? Any underlying assumptions?

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kelvin490 said:
I have two questions, 1. Is it a hidden assumption that the function Φ doesn't change its form for different temperatures? i.e. for different reservoirs we just plug in different temperatures Φ(T1,T2), Φ(T3,T4) but it can never be some other functions for different temperatures. Why?
Your question doesn't make any sense. The fact that it depends on temperatures means that Φ can change its value for different temperatures. It can.
kelvin490 said:
2. Why Φ(T1,T2) can be expressed as ψ(T1)/ψ(T2)? Any underlying assumptions?
My understanding is this is an underlying assumption, at least in this presentation of the material.

kelvin490 said:
In deriving thermodynamic temperature scale, it uses the concept that heat transfer between two reservoirs is the function of the reservoirs' temperatures. i.e. Q1/Q2=Φ(T1,T2). And then further express that Φ(T1,T2)=ψ(T1)/ψ(T2).

I have two questions, 1. Is it a hidden assumption that the function Φ doesn't change its form for different temperatures? i.e. for different reservoirs we just plug in different temperatures Φ(T1,T2), Φ(T3,T4) but it can never be some other functions for different temperatures. Why?

2. Why Φ(T1,T2) can be expressed as ψ(T1)/ψ(T2)? Any underlying assumptions?
See Section 5.3 in Introduction to Chemical Engineering Thermodynamics by Smith and Van Ness.

Chet

1. What is thermodynamic temperature?

Thermodynamic temperature is a measure of the average kinetic energy of the particles in a system, also known as its absolute temperature. It is based on the principles of thermodynamics and is measured in units of kelvin (K).

2. How is thermodynamic temperature derived?

Thermodynamic temperature is derived from the second law of thermodynamics, which states that the efficiency of a heat engine is limited by the ratio of the absolute temperatures of the hot and cold reservoirs. This leads to the definition of the Kelvin scale, where absolute zero (0 K) is the point at which a system has no thermal energy.

3. What is the significance of the Kelvin scale in thermodynamics?

The Kelvin scale is significant in thermodynamics because it is based on the fundamental principles of thermodynamics and allows for consistent and accurate measurements of temperature. It also provides a universal scale that can be used in all areas of science and engineering.

4. How does thermodynamic temperature differ from other temperature scales?

Unlike other temperature scales, such as Celsius and Fahrenheit, thermodynamic temperature is an absolute scale and does not have negative values. It is also based on the properties of a system rather than the properties of a specific substance, making it a more universal and fundamental measurement of temperature.

5. What are some practical applications of thermodynamic temperature?

Thermodynamic temperature is used in a wide range of fields, including physics, chemistry, engineering, and meteorology. It is essential in thermodynamic calculations, such as determining the efficiency of heat engines and predicting the behavior of gases. It is also used in everyday applications, such as measuring the temperature of a patient's body or monitoring the temperature of food during cooking and storage.