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A calorimeter constant (denoted C cal) is a constant that quantifies the heat capacity of a calorimeter. [ 1 ] [ 2 ] It may be calculated by applying a known amount of heat to the calorimeter and measuring the calorimeter's corresponding change in temperature .
Constant-volume calorimetry is calorimetry performed at a constant volume. This involves the use of a constant-volume calorimeter. No work is performed in constant-volume calorimetry, so the heat measured equals the change in internal energy of the system. The heat capacity at constant volume is assumed to be independent of temperature.
A reaction calorimeter is a calorimeter in which a chemical reaction is initiated within a closed insulated container. Reaction heats are measured and the total heat is obtained by integrating heat flow versus time. This is the standard used in industry to measure heats since industrial processes are engineered to run at constant temperatures.
At constant pressure, heat supplied to the system contributes to both the work done and the change in internal energy, according to the first law of thermodynamics. The heat capacity is called C p {\displaystyle C_{p}} and defined as:
It can be shown that the enthalpy of transition can be expressed using the following equation: = where is the enthalpy of transition, is the calorimetric constant, and is the area under the curve. The calorimetric constant will vary from instrument to instrument, and can be determined by analyzing a well-characterized sample with known ...
The left-hand side is the specific heat capacity at constant volume of the material. For the heat capacity at constant pressure, it is useful to define the specific enthalpy of the system as the sum (,,) = (,,) +. An infinitesimal change in the specific enthalpy will then be
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
The heat equation is also widely used in image analysis (Perona & Malik 1990) and in machine learning as the driving theory behind scale-space or graph Laplacian methods. The heat equation can be efficiently solved numerically using the implicit Crank–Nicolson method of (Crank & Nicolson 1947).