Thermodynamics, Statistical Physics, and Quantum Mechanics

116 SOLUTIONS The total energy of the idealgas depends only on thetemperature,which is constant, so the heatabsorbed by the gas ...

117 where the specific heat per one molecule. Integrating (S.4.25.7) yields c) For air we may take (in regularunits, it ismostly ...

118 SOLUTIONS since the initial and final temperatures are thesame. Substitutinginto (S.4.26.1) we find 4.27 Venting (Moscow Phy ...

119 Using theideal gas law we have So The air is mostly nitrogen and oxygen (78% nitrogen and 21% oxygen diatomic gases, sothat ...

120 by and the number ofmoles on the left and right sides of thecylinder, respectively, andusing we obtain the total work and, h ...

121 The heat extracted, is then equal to the difference in initialand final internalenergies ofthe bodies: c) Here we may calcul ...

122 As before, the workextractedequals the change ininternal energy of the bodies, so which is the same as above. 4.30 Heat Capa ...

123 So and Since the time during which the current flows through the wire is the same inbothexperiments, the amount of heattrans ...

124 and We knowthat foran adiabaticprocess So Using wefind and therefore the efficiency is For and the efficiency is b) The work ...

125 4.32 Joule Cycle (Stony Brook) The efficiency of the cycle is given by the work W during the cycle divided by the heat absor ...

126 SOLUTIONS we have Substituting for and byputting(S.4.32.4) into (S.4.32.1)yields The efficiency isthen 4.33 Diesel Cycle (St ...

THERMODYNAMICS AND STATISTICAL PHYSICS 127 The ideal gas law gives Substituting(S.4.33.4) and (S.4.33.5) into (S.4.33.3)gives 4. ...

128 Substituting dVfrom(S.4.34.2) and from(S.4.34.3) into(S.4.34.1), we So, When (S.4.34.5)becomes Ideal Gas and Classical Stati ...

129 The condition alsoimpliesthat Then we may approximate So,(S.4.35.3) becomes where weused the averagenumber ofmolecules inV: ...

4.36 Polarization of Ideal Gas (Moscow Phys-Tech) The potentialenergy of adipole in an electric fieldEis where the angle isbetwe ...

131 where is the Langevin function. For we can expand (S.4.36.3) to obtain Since and we have for thedielectric constant 4.37 Two ...

and 132 We can expand the exponential at hightemperatures so that where The first-order terms are all zeroupon integration, and ...

133 The average force is given by whereFis the freeenergy. So, The minus signindicates an average attraction between the dipoles ...

134 Here we used the factthat the sumdepends only ontemperature, so we can define b) Now we can calculate thetotal entropy of th ...

It can be easily seen that thepressure becomes so 135 and Let us show that isalways nonnegative. This isequivalent to the condit ...