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Thermal Conductivity Measurement
There are a number of possible ways to measure thermal conductivity, each of them suitable for a limited range of materials, depending on the thermal properties and the medium temperature. Three classes of methods exist to measure the thermal conductivity of a sample: steady-state, time-domain, and frequency-domain methods. Steady-state methods In general, steady-state techniques perform a measurement when the temperature of the material measured does not change with time. This makes the signal analysis straightforward (steady state implies constant signals). The disadvantage is that a well-engineered experimental setup is usually needed. Steady-state methods, in general, work by applying a known heat flux, \dot Q (W/m^2), to a sample with a surface area, A(m^2) , and thickness, x (m); once the sample's steady-state temperature is reached, the difference in temperature, \Delta T, across the thickness of the sample is measured. After assuming one-dimensional heat flow and an isotropi ...
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Thermal Conductivity
The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating materials like Rockwool or Styrofoam. Correspondingly, materials of high thermal conductivity are widely used in heat sink applications, and materials of low thermal conductivity are used as thermal insulation. The reciprocal of thermal conductivity is called thermal resistivity. The defining equation for thermal conductivity is \mathbf = - k \nabla T, where \mathbf is the heat flux, k is the thermal conductivity, and \nabla T is the temperature gradient. This is known as Fourier's Law for heat conduction. Although commonly expressed as a scalar, the most general form of ...
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Thermal Diffusivity
In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI derived unit of m2/s. Thermal diffusivity is usually denoted by lowercase alpha (), but , , (kappa), , and are also used. The formula is: :\alpha = \frac where * is thermal conductivity (W/(m·K)) * is specific heat capacity (J/(kg·K)) * is density (kg/m3) Together, can be considered the volumetric heat capacity (J/(m3·K)). As seen in the heat equation, :\frac = \alpha \nabla^2 T, one way to view thermal diffusivity is as the ratio of the time derivative of temperature to its curvature, quantifying the rate at which temperature concavity is "smoothed out". In a sense, thermal diffusivity is a contrasting measure to thermal inertia In thermodynamics, a material's thermal effusivity, thermal inertia or thermal responsivity ...
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Temperature Coefficient
A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property ''R'' that changes when the temperature changes by ''dT'', the temperature coefficient α is defined by the following equation: :\frac = \alpha\,dT Here α has the dimension of an inverse temperature and can be expressed e.g. in 1/K or K−1. If the temperature coefficient itself does not vary too much with temperature and \alpha\Delta T \ll 1, a linear approximation will be useful in estimating the value ''R'' of a property at a temperature ''T'', given its value ''R''0 at a reference temperature ''T''0: :R(T) = R(T_0)(1 + \alpha\Delta T), where Δ''T'' is the difference between ''T'' and ''T''0. For strongly temperature-dependent α, this approximation is only useful for small temperature differences Δ''T''. Temperature coefficients are specified for various applications, including electric and magnetic properties of materials a ...
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Lock-in Amplifier
A lock-in amplifier is a type of amplifier that can extract a signal with a known carrier wave from an extremely noisy environment. Depending on the dynamic reserve of the instrument, signals up to a million times smaller than noise components, potentially fairly close by in frequency, can still be reliably detected. It is essentially a homodyne detector followed by low-pass filter that is often adjustable in cut-off frequency and filter order. The device is often used to measure phase shift, even when the signals are large, have a high signal-to-noise ratio and do not need further improvement. Recovering signals at low signal-to-noise ratios requires a strong, clean reference signal with the same frequency as the received signal. This is not the case in many experiments, so the instrument can recover signals buried in the noise only in a limited set of circumstances. The lock-in amplifier is commonly believed to have been invented by Princeton University physicist Robert H. Di ...
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Phase (waves)
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or 2\pi as the variable t completes a full period. This convention is especially appropriate for a sinusoidal function, since its value at any argument t then can be expressed as \phi(t), the sine of the phase, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.) Usually, whole turns are ignored when expressing the phase; so that \phi(t) is also a periodic function, with the same period as F, that repeatedly scans the same range ...
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Resistance Temperature Detector
Resistance thermometers, also called resistance temperature detectors (RTDs), are sensors used to measure temperature. Many RTD elements consist of a length of fine wire wrapped around a heat-resistant ceramic or glass core but other constructions are also used. The RTD wire is a pure material, typically platinum (Pt), nickel (Ni), or copper (Cu). The material has an accurate resistance/temperature relationship which is used to provide an indication of temperature. As RTD elements are fragile, they are often housed in protective probes. RTDs, which have higher accuracy and repeatability, are slowly replacing thermocouples in industrial applications below 600 ° C. Resistance/temperature relationship of metals Common RTD sensing elements for biomedical application constructed of platinum (Pt), nickel (Ni), or copper (Cu) have a repeatable resistance versus temperature relationship (''R'' vs ''T'') and operating temperature range. The ''R'' vs ''T'' relationship is ...
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3ω-method
The 3ω-method (3 omega method) or 3ω-technique, is a measurement method for determining the thermal conductivities of bulk material (i.e. solid or liquid) and thin layers. The process involves a metal heater applied to the sample that is heated periodically. The temperature oscillations thus produced are then measured. The thermal conductivity and thermal diffusivity of the sample can be determined from their frequency dependence. Theory The 3ω-method can be accomplished by depositing a thin metal structure (generally a wire or a film) onto the sample to function as a resistive heater and a resistance temperature detector (RTD). The heater is driven with AC current at frequency ω, which induces periodic joule heating at frequency 2ω (since P = I^R) due to the oscillation of the AC signal during a single period. There will be some delay between the heating of the sample and the temperature response which is dependent upon the thermal properties of the sensor/sample. This te ...
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Density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of density across different s ...
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Kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. It means 'one thousand grams'. The kilogram is defined in terms of the second and the metre, both of which are based on fundamental physical constants. This allows a properly equipped metrology laboratory to calibrate a mass measurement instrument such as a Kibble balance as the primary standard to determine an exact kilogram mass. The kilogram was originally defined in 1795 as the mass of one litre of water. The current definition of a kilogram agrees with this original definition to within 30 parts per million. In 1799, the platinum '' Kilogramme des Archives'' replaced it as the standard of mass. In 1889, a cylinder of platinum-iridium, the International Prototype of the Kilogram (IPK), became the standard of the unit of mass for ...
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Joule
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied. It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889). Definition In terms of SI base units and in terms of SI derived units with special names, the joule is defined as One joule can also be defined by any of the following: * The work required to move an electric charge of one coulomb through an electrical potential difference of one volt, or one coulomb-volt (C⋅V). This relationship can be used to define the volt. * The work required to produce one watt of power for one second, or one watt-second (W⋅s) (compare kilowatt-hour, which is 3.6 megajoules). This relationshi ...
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Heat Capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity, found by dividing the heat capacity of an object by its mass. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume. In architecture and civil engineering, the heat capacity of a building is often referred to as its thermal mass. Definition Basic definition The heat capacity of an object, denoted by C, is the limit : C = \lim_\frac, where \Delta Q is the amount of heat that must be added to the object (of mass ''M'') in order to raise its temperature by \Delta T. The value of this parameter usually varies considerably depending on ...
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Laser Flash Method
The laser flash analysis or laser flash method is used to measure thermal diffusivity of a variety of different materials. An energy pulse heats one side of a plane-parallel sample and the resulting time dependent temperature rise on the backside due to the energy input is detected. The higher the thermal diffusivity of the sample, the faster the energy reaches the backside. A laser flash apparatus (LFA) to measure thermal diffusivity over a broad temperature range, is shown on the right hand side. In a one-dimensional, adiabatic case the thermal diffusivity a is calculated from this temperature rise as follows: : a = 0.1388 \cdot \frac Where * a is the thermal diffusivity in cm2/s * d is the thickness of the sample in cm * t_ is the time to the half maximum in s Measurement principle The laser flash method was developed by Parker et al. in 1961. In a vertical setup, a light source (e.g. laser, flashlamp) heats the sample from the bottom side and a detector on top detec ...
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