Specific heat at constant volume

Available data on the thermodynamic and transport properties of carbon dioxide have been reviewed and tables compiled giving specific volume, enthalpy, and entropy values for carbon dioxide at temperatures from 255 K to 1088 K and at pressures from atmospheric to 27,600 kPa (4,000 psia). Diagrams of compressibiHty factor, specific heat at constant pressure, specific heat at constant volume, specific heat ratio, velocity of sound in carbon dioxide, viscosity, and thermal conductivity have also been prepared (5). 

Cp = specific heat at constant pressure c = specific heat at constant volume... 

The integrated terms are simply the specific heat of the unit mass of adsorbent and its associated adsorbate. The specific heat at constant volume has been used for the adsorbate since, theoretically, there is no expansion of the adsorbate volume and the heat required to raise the temperature is the change in internal energy. In practice there will be some expansion and a pessimistically high estimate could use the specific heat at constant pressure The specific heat of the adsorbed phase is in any case difficult to estimate and it is common to approximate it to that of saturated liquid adsorbate at the same temperature. 

Blend the specific heats at constant volume in the same maimer. 

The measurement of the specific heat at constant volume is attended with considerable difficulty, because the thermal capacity of a vessel strong enough to contain the gas after heating has a value much greater than that of the thermal capacity of the enclosed gas. 

SQ) = (yp h1),- ( Q)p = (r4l%-Thus, cv, cp are the amounts of heat absorbed per unit increase of temperature at constant volume and at constant pressure respectively. They are the specific heats at constant volume and at constant jwessare respectively. 

Corollary 1.—The specific heat at constant volume of an ideal... 

We first assume that the specific heat at constant volume is independent of temperature (Clausius). 

A. Michels and J. Strijland, "The Specific Heat at Constant Volume of Compressed Carbon Dioxide , Physica, 18, 613-628 (1952). 

From statistical calculations01 the value of iij has been given as (9y — 5)/8 (where y = Cp/Cv, the ratio of the specific heat at constant pressure to the specific heat at constant volume). 

The heat capacity of a substance can differ, depending on which are the variables held constant, with the quantity being held constant usually being denoted with a subscript. For example, the specific heat at constant pressure is commonly denoted cP, while the specific heat at constant volume is commonly denoted cv ... 

The experimental data usually give the specific heat at constant pressure cP. Theories usually refer to the specific heat at constant volume cv. The specific heat cP is greater than cv by a factor (1 + jgT), where f5 is the volumetric coefficient of thermal expansion and yG is the so-called Griineisen parameter ... 

Cp specific heat at constant pressure, J/(kg °C) Cv specific heat at constant volume, J / (kg °C) Cves specific heat of vessel, kJ/°C... 

Table 8 displays the computed internal energy and specific heat at constant volume. The fact that these agree well with each other, and with experiment, despite the differences in local structure of liquids based on the two potentials emphasizes the insensitivity of thermodynamic properties (except pressure) to structural details. 

Any characteristic of a system is called a property. The essential feature of a property is that it has a unique value when a system is in a particular state. Properties are considered to be either intensive or extensive. Intensive properties are those that are independent of the size of a system, such as temperature T and pressure p. Extensive properties are those that are dependent on the size of a system, such as volume V, internal energy U, and entropy S. Extensive properties per unit mass are called specific properties such as specific volume v, specific internal energy u, and specific entropy. s. Properties can be either measurable such as temperature T, volume V, pressure p, specific heat at constant pressure process Cp, and specific heat at constant volume process c, or non-measurable such as internal energy U and entropy S. A relatively small number of independent properties suffice to fix all other properties and thus the state of the system. If the system is composed of a single phase, free from magnetic, electrical, chemical, and surface effects, the state is fixed when any two independent intensive properties are fixed. 

Since the specific heat at constant volume is given by the temperature derivative of the internal energy as defined in Eq. (1.7), the specific heat ofa molecule, is represented by... 

The specific heat at constant volume can be obtained directly from the partition function... 

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