An Introduction to Equilibrium Thermodynamics by Bernard Morrill

By Bernard Morrill

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T h e theory of elasticity is not usually presented in vector (1st o r d e r tensor) c o n c e p t s but in t e n s o r (2nd o r d e r tensor) forms. W e usually deal with stresses, not with forces. T h e stress-strain relationship is not a simple o n e . N o a t t e m p t will be m a d e here to deal with general concepts. W e shall consider only the case of w o r k d o n e by an elastic system w h e n the stresses and strains are e x p r e s s e d as principle stresses and strains. 1) w h e r e the σ / s and e/s are principle stresses and strains respectively.

In the same m a n n e r volume and t e m p e r a t u r e can be d e m o n s t r a t e d to be properties. W e have merely shown that the p r e s s u r e as given by the perfect gas equation has an exact differential. W e h a v e not established a general proof. T h e definition that a property is governed by its end states will serve as the necessary and sufficient conditions for determining a property. So far, the properties which have b e e n e n c o u n t e r e d are the internal energy, pressure, t e m p e r a t u r e , v o l u m e , m a s s , and heat capacity.

T h e k n o w n changes of internal energy, heat transfer, and w o r k are tabulated. D e t e r m i n e t h e u n k n o w n s for each process of t h e system. Process 1-2 2-3 3-4 4-1 t/(BTU) -100 -50 ß(BTU) 150 50 -50 -75 W(BTU) -150 T h e work process from 1-2 is given by 1 ^2 = ,02-,Δί/2 1 5 0 + 100 250 B T U T h e w o r k process from 2 - 3 is 2 2^3 = 2 ^ = β3-2Δί/3 50 + 50 100 B T U S W e c a n n o t determine either ZW4 or 3 Δ ί / 4 for the m o m e n t , so w e p a s s on to the process 4 - 1 .

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