# Introduction to the renormalization group and critical by Pierre Pfeuty

By Pierre Pfeuty

E-book by means of Pfeuty, Pierre, Toulouse, Gerard

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44 x 10 "' C - m . Therefore. lc (c) A rr~oleculcwith a pcrnlanenr dipole Illolrlent will induce a dipole moment In a neighhrlring molecule. (d) The instantaneous dipole-dipule correlation strr)wn herc is what leudr to a Lundon attraction between all atoms and mvlecules in Figi~~-e 2. I b i ~to attractive. 16b). Both ~riolcculesrotate in thc gas phase, and if we were to avtrnge both dipoles randomly ovcr their oricntn~iuns,the dipole-dipole interactions would average out to 7cro. Because diikrcnt orientations have difl-ercnt energies, they do no1 occur to equal extents.

X l l i ' ~ ' r ' . k gm - ' j 2 '1111\ ~lu~r~rrlcrtl rck1111111ily YCL'III exceedingly small, but remerltber that wwearc cnl. C I I I I I ~ I I I ~ t 'id,, , ( { rJ. 5 x 10 J . 1 x 10 'I 3 at 300 K. ;i perrtlilnent dipole morrietlt. 33 rcyuircs [hilt holh ~ncllcu~ilcs Even il- one nlr~leculcdocs 1101 h:tvc ;I pcrnxjncnt dipole nloment, thc one withnut a permnrletlt dipole Inonierll wlll have ;I dipcjlc molncnl induced by the other. A dipole moment can be induced in n niolcculc that docs t~othavc a permanent d i p l e motnerlt bccause all atoms and molecules are pulrrrizmhlr.

K I . 15 K for any gas at a sul~ticienilylow prcswrt. 020 attn. 010 alm. rhc,dlines). 2 A plot of experinlcnpl values of PF P for H,(g, tclrj\cc\). 15 K. atrn as P + O (ideal behavior). 2 'I'he values of the molar gas constant R in variuur unit?. bar,mol-l . K-' 2-2. The van der Waals Equation and the Rcdlich-Kwong Equation Are Examples of Two-Parameter Equations clf Stdtc The idral-gas equation is valid for all gasc5 at sufficiently low pressures. 3. torand is denoted hy Z . Notc that % = I under all co~ldiiionsfur an ideal gas.