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The Concept of Temperature in Thermodynamics

The Kelvin scale defines absolute temperature in thermodynamics, based on a Carnot engine model. Temperature, an intensive property, is crucial for understanding thermal equilibrium, as stated by the zeroth law. Local thermodynamic equilibrium allows for temperature variability within systems, and temperature scales like Celsius and Kelvin provide consistent measurements. Heat capacity and specific heat are key in energy transfer.

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1

Definition of Temperature in Thermodynamics

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Temperature in thermodynamics is defined based on the Carnot engine's reversible cycle and heat exchange between two reservoirs.

2

Function of a Carnot Engine

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A Carnot engine absorbs heat from a high-temp reservoir, performs work, and releases heat to a low-temp reservoir without energy loss.

3

Equation Relating Temperature and Heat Exchange

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The equation T₁/T₂ = Q₁/Q₂ relates the absolute temperatures (T) of reservoirs to the heat (Q) exchanged, independent of material properties.

4

Temperature is an ______ property, meaning its value doesn't change with the system's size.

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intensive

5

Temperature is defined mathematically as a partial derivative of internal energy with respect to ______, while other properties remain constant.

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entropy

6

The zeroth law supports the use of temperature as a reliable measure for determining ______ equilibrium between systems.

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thermal

7

Global vs. Local Thermodynamic Equilibrium

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Global equilibrium: entire system uniform. Local equilibrium: smaller regions uniform, each with own temp.

8

Temperature as a Local Variable

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In local thermodynamic equilibrium, temperature varies within system, defining local state variables.

9

Importance in Non-Homogeneous Systems

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Local equilibrium crucial for analyzing temperature gradients and heat transfer in systems lacking uniformity.

10

Temperature measures the ______ or thermal energy of a system, which is an abstract concept not specific to any scale.

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'hotness'

11

To gauge this intrinsic property, various ______ temperature scales have been created.

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empirical

12

Two systems with identical temperatures are in ______ equilibrium, preventing net heat transfer.

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thermal

13

Heat flows from the ______ system to the cooler one until temperatures equalize if they are not the same.

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hotter

14

Heat transfer can occur through ______, ______, or ______.

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conduction convection radiation

15

Physical basis for 'hotness'

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Wien's displacement law correlates black body radiation peak wavelength with temperature, defining 'hotness'.

16

Temperature's one-dimensional manifold

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Temperature represents a one-dimensional manifold, indicating a single value describes thermal state.

17

Monotonic vs. Linear relationship in temperature scales

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Temperature scales are consistent due to monotonic, not necessarily linear, relationships between them.

18

The ______ is measured by the heat amount needed to elevate a body's temperature by a specific increment, usually one degree.

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heat capacity

19

Heat capacity varies depending on whether the heat transfer takes place at ______ or ______.

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constant volume constant pressure

20

______, also known as specific heat, is the heat necessary to increase the temperature of one mass unit of a substance by one degree Celsius or Kelvin.

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Specific heat capacity

21

Phase changes and ______ can influence the heat capacity of a material.

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chemical reactions

22

Origin of temperature measurement

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Began with development of thermometers and temperature scales.

23

Kelvin scale starting point

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Starts at absolute zero, where thermal motion ceases.

24

Celsius to Kelvin conversion

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Kelvin is Celsius plus 273.15 degrees.

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The Kelvin Scale and the Absolute Temperature

Temperature is a key concept in thermodynamics, precisely defined by Lord Kelvin in the 19th century. This definition arises from the theoretical model of a Carnot engine—a perfect heat engine that operates on a reversible cycle between two heat reservoirs. The engine absorbs heat from a high-temperature reservoir, performs work, and releases some heat to a low-temperature reservoir without any loss of energy in the process. The Kelvin scale is based on this model, where the absolute temperatures of the reservoirs are proportional to the amounts of heat exchanged. The equation T₁/T₂ = Q₁/Q₂ (where Q represents heat absorbed or released and T represents absolute temperature) defines the scale, setting the stage for measuring temperature independent of material properties, with the unit of Kelvin (K) as the standard.
Science laboratory with digital thermometer in beaker with blue liquid, blue flame under glass flask, test tubes with colored liquids on shelf.

Intensive Properties and the Zeroth Law of Thermodynamics

Temperature is an intensive property, which means it does not vary with the size or extent of a system. It is mathematically defined as a partial derivative of an extensive property, such as internal energy, with respect to another, like entropy, while keeping other extensive properties constant. The zeroth law of thermodynamics establishes a foundational principle for temperature measurement: if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law validates the use of temperature as a consistent and reliable indicator of thermal equilibrium across different systems.

Local Thermodynamic Equilibrium and Temperature Variability

While global thermodynamic equilibrium may not always be present, systems can achieve local thermodynamic equilibrium within smaller regions. In such cases, each region can be characterized by its own temperature, allowing temperature to be a local variable within a system. This is particularly important in non-homogeneous systems where temperature gradients are present. The principle of local thermodynamic equilibrium is essential for analyzing and understanding the temperature distribution and heat transfer within complex systems.

The Concept of Hotness and Temperature Measurement

Temperature quantifies the 'hotness' or thermal energy of a system, an abstract concept that is not tied to any particular scale. Various empirical temperature scales have been developed to measure this intrinsic property. When two systems share the same temperature, they are in thermal equilibrium, and no net heat transfer occurs between them. If their temperatures differ, heat will naturally flow from the hotter to the cooler system until equilibrium is established. This transfer can take place via conduction, convection, or radiation.

Thermodynamic Equilibrium and Temperature Scales

At thermodynamic equilibrium, all empirical thermometers should register the same temperature for a system. This consistency does not rely on a linear relationship between different temperature scales but rather on a monotonic relationship. The physical basis for the concept of temperature, or 'hotness', is supported by Wien's displacement law, which correlates the peak wavelength of radiation emitted by a black body to its temperature. This law substantiates the one-dimensional manifold of temperature, which is a fundamental aspect of the concept of temperature.

Heat Capacity and Energy Transfer

Heat capacity is the property of a material that indicates its ability to absorb heat without a significant change in temperature. It is quantified as the amount of heat required to change the temperature of a body by a certain amount, typically one degree. This property is dependent on the conditions under which heat transfer occurs, such as constant volume or constant pressure, and can be affected by phase changes or chemical reactions. Specific heat capacity, or simply specific heat, is a related concept that denotes the heat required to raise the temperature of a unit mass of a substance by one degree Celsius or Kelvin.

Modern Temperature Measurement and Units

The methods and units for measuring temperature have evolved over time, beginning with the development of thermometers and scales like Fahrenheit and Celsius. In contemporary scientific and engineering contexts, the Celsius and Kelvin scales are predominantly used, with Kelvin being the SI base unit for temperature. The Kelvin scale starts at absolute zero, the theoretical point where all thermal motion ceases, and is offset from Celsius by 273.15 degrees. In the United States, the Rankine scale, which is analogous to the Fahrenheit scale but adjusted for absolute temperatures, is sometimes used in engineering applications.