Volumetric coefficient of thermal expansion

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 ... 

The transition at 19° C involves an expansion of 0.0058 cm3/g (Clark and Muus). Sincethe transition temperatureincreaseswith pressure by about 0.013° C per atmosphere (Beecroft and Swenson), the latent heat is about 3.2 cal/g. These values are for the crystal and would be reduced in proportion to the crystalline content. The transition at 30° C is only about one-tenth as large. The over-all increase in entropy at these transitions is about 0.0108 cal deg-1g-1. The portion due to the increase in volume is (a// ) A V, where a is the volumetric coefficient of thermal expansion and / is the compressibility. Since the compressibility of the crystal is not known, this quantity is somewhat uncertain. Using the average of the values of a (Quinn, Roberts, and Work) and p (Weir, 1951) for the whole polymer above and below the transitions, it appears that (a/P)A V is about 0.0041 cal deg 1g 1. The entropy of the transition corrected to constant volume is, therefore, about 0.0067 cal deg g-1. 

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

The effect of temperature and pressure on volume is quantified by two coefficients, the volumetric coefficient of thermal expansion, and the coefficient of isothermal compression. The volumetric coefficient of thermal expansion is defined as... 

Calculate the volumetric coefficient of thermal expansion of acetone at 20 "C and the percent increase in volume upon a temperature increase fi-om 20 °Cto30 °C at constant pressure. 

Here, the volumetric coefficient of thermal expansion a is defined as the fractional change in volume per unit change in temperature under constant pressure conditions. The linear coefficient of thermal expansion A, is the fractional change in length (or any linear dimension) per unit change in temperature while the stress on the material remains constant. For isotropic materials, a = 3A,. 

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