Introduction To Statistical Mechanics by James Rice

By James Rice

The purpose and scope of this publication is indicated within the introductory bankruptcy. the writer isn't really ignorant of the truth that the scholar he had in brain whilst he wrote it's not going to learn a few components of it and not using a severe psychological attempt; the inevitably mathematical kind of the arguments involves that consequence. yet he feels definite that any pupil with the common mathematical apparatus received within the first years of a school technology direction won't locate it very unlikely to stick to the main points of the remedy, and as a lot suggestions as attainable is supplied in explanatory appendices, in verbal interpretation and representation. within the proofs no .steps are passed over. On that account the content material of topics handled has needed to be constrained : another way the e-book might have grown to a size wrong for the kind of reader whom it truly is meant to aid. the issues handled are excited by platforms in statistical equilibrium, even though a brief appendix refers back to the topic of collision-frequency in gases and its relating chemical reactions.

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C) Temperature reached = 5Γο/4. Heat absorbed = —CvTo/4. (d) Temperature returns to To. Heat absorbed = —CpTo/4. With the given values of Cp, Cv, the work done per cycle is then 7o(l + 2-1 - 1-25 - 1-75) = 0-1 T0 cal mole"1. The heat absorbed per cycle is 3·17ο cal mole -1 . The efficiency of the cycle is 0 Ί / 3 Ί . The efficiency of a Carnot engine working Thermal engines 59 between 3Γο/2 and To is 1/3, thus the required ratio is 3/31 = 0-0^68. 31. A given mass of a monatomic ideal gas undergoes the following cycle of operations: (1) heating at constant volume Vo from temperature To to 2To; (2) isothermal expansion to volume 2V0; (3) cooling at constant volume 2V0 from 2T0 to T0; (4) iso­ thermal compression to the initial state.

Determine the efficiency of the Joule cycle, made up of two processes at constant pressures pi, pi joined by two adiabatic processes. Answer, Let the initial state be the state at the end of the isobaric compression. Then βι = 0 , ( Γ 3 - Γ 2 ) ; Hence But Thus v = 1 —— 1 T\ p\~y = T\ p\-y I β2 = 0 , ( Γ 4 - 2 ι ) . — T3-T2 and T\ p\-* = T* p\-*. 2) ( r ~ 1 ) r . 30. A perfect gas has Cv = 1 and CV = 5 cal deg - 1 mole -1 . The gas is (a) heated reversibly at constant volume until p is 6/5 of its initial value; (b) heated reversibly at constant pressure until V is 5/4 of the initial value; (c) cooled reversibly at constant volume until p returns to its initial value; (d) cooled reversibly at constant pressure to the initial conditions.

Answer. 5000 g are 5000/32 = 156-25 moles. Assuming oxygen to be an ideal gas, the initial pressure is then p = 3-897 x 105 dyne cm-2. In process (a), νΤα=ρΔν=-1-95 X 105 J (negative because it is work done on the gas). The final tempera­ ture is 150°K. The thermal capacity Cv is given by (66) to be (5/2>iÄ = (5/2) x 156-25 x 8-314 = 3248 J deg-1, thus, from (45), äUa = -4-87 X 10* J, and Qa = Δ[/ώ + Wa = —6-82 X 105 J. In process (b), from (58), Wb = -nRTlnl = -2-70 X 10* J. This is also the heat exchanged because, at constant temperature, there is no change of internal energy.

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