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The classical equipartition theorem predicts that the heat capacity ratio (γ) for an ideal gas can be related to the thermally accessible degrees of freedom (f) of a molecule by = +, =. Thus we observe that for a monatomic gas, with 3 translational degrees of freedom per atom: γ = 5 3 = 1.6666 … , {\displaystyle \gamma ={\frac {5}{3}}=1. ...
The corresponding expression for the ratio of specific heat capacities remains the same since the thermodynamic system size-dependent quantities, whether on a per mass or per mole basis, cancel out in the ratio because specific heat capacities are intensive properties. Thus:
In those contexts, the unit of heat capacity is 1 BTU/°R ≈ 1900 J/K. [5] The BTU was in fact defined so that the average heat capacity of one pound of water would be 1 BTU/°F. In this regard, with respect to mass, note conversion of 1 Btu/lb⋅°R ≈ 4,187 J/kg⋅K [ 6 ] and the calorie (below).
The method proceeds by calculating the heat capacity rates (i.e. mass flow rate multiplied by specific heat capacity) and for the hot and cold fluids respectively. To determine the maximum possible heat transfer rate in the heat exchanger, the minimum heat capacity rate must be used, denoted as C m i n {\displaystyle \ C_{\mathrm {min} }} :
The Rüchardt experiment, [1] [2] [3] invented by Eduard Rüchardt, is a famous experiment in thermodynamics, which determines the ratio of the molar heat capacities of a gas, i.e. the ratio of (heat capacity at constant pressure) and (heat capacity at constant volume) and is denoted by (gamma, for ideal gas) or (kappa, isentropic exponent, for real gas).
A hot fluid's heat capacity rate can be much greater than, equal to, or much less than the heat capacity rate of the same fluid when cold. In practice, it is most important in specifying heat-exchanger systems, wherein one fluid usually of dissimilar nature is used to cool another fluid such as the hot gases or steam cooled in a power plant by a heat sink from a water source—a case of ...
The heat capacity ratio, or adiabatic index, is the ratio / of the heat capacity at constant pressure to heat capacity at constant volume. It is sometimes also known ...
The proportionality factor is the specific heat capacity, which depends on the nature of the substance, but which was not described until some time after Richmann's discovery by Joseph Black. Thus, the validity of the formula is limited to mixtures of the same substance, since it assumes a uniform specific heat capacity. [9]