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Volumetric heat capacities in polyatomic gases vary widely, however, since they are dependent largely on the number of atoms per molecule in the gas, which in turn determines the total number of atoms per volume in the gas. The volumetric heat capacity is defined as having SI units of J/(m 3 ⋅K).
Table of specific heat capacities at 25 °C (298 K) unless otherwise noted. [citation needed] Notable minima and maxima are shown in maroon. Substance Phase Isobaric mass heat capacity c P J⋅g −1 ⋅K −1 Molar heat capacity, C P,m and C V,m J⋅mol −1 ⋅K −1 Isobaric volumetric heat capacity C P,v J⋅cm −3 ⋅K −1 Isochoric ...
Quantity (common name/s) (Common) symbol/s Defining equation SI unit Dimension Temperature gradient: No standard symbol K⋅m −1: ΘL −1: Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer
The heat capacity can usually be measured by the method implied by its definition: start with the object at a known uniform temperature, add a known amount of heat energy to it, wait for its temperature to become uniform, and measure the change in its temperature.
This is a derivation to obtain an expression for for an ideal gas. An ideal gas has the equation of state: = where P = pressure V = volume n = number of moles R = universal gas constant T = temperature. The ideal gas equation of state can be arranged to give:
All values refer to 25 °C and to the thermodynamically stable standard state at that temperature unless noted. Values from CRC refer to "100 kPa (1 bar or 0.987 standard atmospheres)".
However, in a process without a constant volume, the heat addition affects both the internal energy and the work (i.e., the enthalpy); thus the temperature changes by a different amount than in the constant-volume case and a different heat capacity value is required.
To achieve the same increase in temperature, more heat energy is needed for a gram of that substance than for a gram of a monatomic gas. Thus, the specific heat capacity per mole of a polyatomic gas depends both on the molecular mass and the number of degrees of freedom of the molecules. [27] [28] [29]