Specific heat, definition

The variation of specific heat with temperature was discovered by Dulong and Petit in 1819. It explains why so many different heat units exist (cf. 5), and requires the definition of specific heat to be so framed as to allow for this variation. For this purpose we replace the finite changes by infinitesimal ones. If SQ units of heat are absorbed when unit mass of a substance is raised in temperature from 6— SO) to 0- - SO) underspecified conditions, the true specific heat at the temperature 0 is ... 

In the SI system, the unit of heat is taken as the same as that of mechanical energy and is therefore the Joule. For water at 298 K (the datum used for many definitions), the specific heat capacity Cp is 4186.8 J/kg K. 

In all of these systems, by definition, the specific heat capacity of water is unity. It may be noted that, by comparing the definitions used in the SI and the mks systems, the kilocalorie is equivalent to 4186.8 J/kg K. This quantity has often been referred to as the mechanical equivalent of heat J. 

The temperature profile of a planetary atmosphere depends both on the composition and some simple thermodynamics. The temperature decreases with altitude at a rate called the lapse rate. As a parcel of air rises, the pressure falls as we have seen, which means that the volume will increase as a result of an adiabatic expansion. The change in enthalpy H coupled with the definition of the specific heat capacity... 

Students often get the terms, heat, specific heat and temperature confused. Here are the formal definitions ... 

The specific heat capacity commonly has units of J/g-K. Because of the original definition of the calorie, the specific heat capacity of water is 4.184 J/g-K. If the specific heat capacity, the mass, and the change of temperature are all known, the amount of energy absorbed can easily be calculated. 

For the plug flow reactor or any similar adiabatic system, it is also possible to define an average specific heat that takes its explicit definition from... 

If the heat capacity of a chemically complex melt can be obtained by a linear summation of the specific heat of the dissolved oxide constituents at all T (i.e., Stebbins-Carmichael model), the melt is by definition ideal. The addition of excess Gibbs free energy terms thus implies that the Stebbins-Carmichael model calculates only the ideal contribution to the Gibbs free energy of mixing. 

No thermodynamic signature at Tg is evident in specific heat data at equilibrium, but a peak is observed under nonequilibrium conditions and is often taken as the definition of the glass transition. Unfortunately, this nonequilibrium peak cannot be addressed within the LCT of glass formation. We strictly avoid a discussion of the specific heat, given the complications of interpreting these data for polymer materials and the omission of the important vibrational component in the LCT treatment. 

This equation does not imply that specific heats are constant—indeed, they are generally functions of temperature. Rather, there is not a specific-heat derivative in Eq. 3.208, because of the definition of specific heat, Eq. 3.207. 

The specific heat of any substance is the number of calories required to raise one gram of it 1°C. From our definition of the calorie, it follows that the specific heat of water is 1 cal/g °C. 

The specific and molar heat capacities of some common substances are given in Table 6.1. Note that, although the values of the specific heat capacities are listed in joules per degree Celsius per gram (J-(°C) 1 -g 1), they could equally well be reported in joules per kelvin per gram (J-K 1-g ) with the same numerical values, because the size of the Celsius degree and the kelvin are the same. We can calculate the heat capacity of a substance from its mass and its specific heat capacity by rearranging the definition Cs = dm into C = mCs. Then we can use... 

The volume of the mixture which burns in unit time on 1 m2 of the flame is equal to u by the definition of the normal velocity its specific heat is equal to... 

By definition, the heat capacity of a system is the amount of energy required to raise its temperature by 1 K. The unit is J KT1. To allow calculations and comparisons, the specific heat capacity is more commonly used ... 

We are asked to calculate the specific heat of copper. We can easily do this using the definition of specific heat, ensuring that we use the proper SI units. 

In conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

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