By Thomas Flynn
Written through an engineering advisor with over forty eight years of expertise within the box, this moment version presents a reader-friendly and thorough dialogue of the basic rules and technological know-how of cryogenic engineering together with the houses of fluids and solids, refrigeration and liquefaction, insulation, instrumentation, common fuel processing, and safeguard in cryogenic procedure layout.
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Additional resources for Cryogenic Engineering, Second Edition, Revised and Expanded
000657 cal=g. than do monatomic molecules. As a ﬁrst approximation, CV increases by R for each additional atom in the molecule. This is a consequence of the principle of equipartion of energy: the value of CV increases by (1=2)R for each additional mode by which energy can be soaked up (three translational modes plus one rotational and one vibrational per bond formed). This holds well for diatomic molecules [CV ¼ (5=2)R, CP ¼ (7=2)R], but as more atoms are added it does not work so well. The vibrational modes and rotational modes are not completely independent in more complex molecules.
3. The Constant-Pressure Case The ﬁrst law in differential form can be combined with the expression for work under constant pressure, dW ¼ P0 dV, to yield dQ À dW ¼ dU Thus, dQ ¼ P0 dV þ dU where P0 ¼ the constant system pressure. Rearranging gives QP ¼ P0 ðV2 À V1 Þ þ DU ¼ P0 V2 À P0 V1 þ U2 À U1 ¼ ðP0 V2 þ U2 Þ À ðP0 V1 þ U1 Þ and since P0 ¼ P2 ¼ P1 ¼ constant, this may be rewritten as QP ¼ ðP2 V2 þ U2 Þ À ðP1 V1 ¼ U1 Þ which, from the deﬁnition of enthalpy, H U þ PV QP ¼ H 2 À H 1 ¼ DH Thus, at constant pressure, Q ¼ ðDHÞP Differentiating this expression with respect to temperature suggests the function dQ dH ¼ CP dT P dT P which is the deﬁnition of heat capacity at constant pressure.
R is in units per mole, and k is in units per molecule. Both R and k are scaling factors between temperature and energy. For physicists, E ¼ kT. For chemists, it is PV ¼ RT, where the product PV is energy. 1. We have already deﬁned the heat capacities Cv and Cp. The ideal gas derivation can also breathe some life into these two important quantities. Heat capacity describes the ability of some substance to ‘‘soak up’’ energy. Consider the molecules of a monatomic ideal gas. The only way a monatomic gas can soak up energy is to increase in kinetic energy.
Cryogenic Engineering, Second Edition, Revised and Expanded by Thomas Flynn