Isobaric isochoric

In an isothermal process, heat must be added during an expansion and removed during a compression to keep the temperature constant. We will describe this more fully as we now calculate the heat added or removed in isobaric, isochoric, and isothermal processes. 

Work, heat, AU, AH, Isothermal, isobaric, isochoric, adiabatic Hess law, calorimetry, T-dependence of enthalpy Second Law 5 lectures... 

The entropy, Spontaneous vs non-spontaneous, Reversible and irreversible processes, Calculation of entropy changes (Isothermal, isobaric, isochoric, adiabatic), Phase changes at equilibrium, Trouton s rule, Calculation for irreversible processes... 

Here, V denotes specific volume, K denotes bulk modulus, subscripts P,V, S and T denote isobaric, isochoric, isentopic and isothermal conditions, respectively s is the second-rank strain tensor, and C is the fourth-rank elastic tensor. 

Typical uncertainties in density are 0.02% in the liquid phase, 0.05% in the vapor phase and at supercritical temperatures, and 0.1% in the critical region, except very near the critical point, where the uncertainty in pressure is 0.1%. For vapor pressures, the uncertainty is 0.02% above 180 K, 0.05% above 1 Pa (115 K), and dropping to 0.001 mPa at the triple point. The uncertainty in heat capacity (isobaric, isochoric, and saturated) is 0.5% at temperatures above 125 K and 2% at temperatures below 125 K for the liquid, and is 0.5% for all vapor states. The uncertainty in the liquid-phase speed of sound is 0.5%, and that for the vapor phase is 0.05%. The uncertainties are higher for all properties very near the critical point except pressure (saturated vapor/liquid and single pliase). The uncertainty in viscosity varies from 0.4% in the dilute gas between room temperature and 600 K, to about 2.5% from 100 to 475 K up to about 30 MPa, and to about 4% outside this range. Uncertainty in thermal conductivity is 3%, except in the critical region and dilute gas which have an uncertainty of 5%. 

This computer program calculates a batch reactor working under different conditions (adiabatic, isothermal, isobaric, isochoric) and carries out a sensitivity analysis of the reaction mechanisms. It is part of the CHEMKIN system. 

Under isothermal-isobaric-isochoric conditions, M is solely a function of and E. The dependence on E at constant defines a (normal) physical part whereas the dependence of M on at constant E may be referred to as the chemical contribution to a change in M. The field dependence of the total moment may then be expressed as... 

The basic idea is to develop expressions for common thermodynamic quantities in terms of fluctuations in a system open to all species. The key lies in the fact that the fluctuating quantities characteristic of the grand canonical ensemble can then be transformed into expressions, which provide properties representative of the isothermal isobaric ensemble. Using an equivalence of ensembles argument, one can then consider these fluctuations to represent properties of small microscopic local regions of the solution of interest. This approach can be used to understand many properties of isobaric, isochoric, or osmotic systems in terms of particle number (and energy) fluctuations. 

Isobars, isochores, isotherms, and isentropes express virtually zero Ix, and Ix(, respectively. The qualifier virtually is added to acknowledge the effects of fluctuations—these always impose some uncertainty for a system. Isochores further express while for isentropes, 0. Not-so-... 

Note the qualifier not necessarily. Sometimes the most direct pathway is the most economical. More to the point, the special pathways of Chapter 4 offer the maximum economy in one or more state variables. For isobaric, isochoric, adiabatic, and isothermal cases, Ix p, Ix<, and 0, respectively for every path of a closed system, Ix = 0. Note that special pathways afford straight-line representations in select planes, for example, isobaric and isochoric in pV, and adiabatic in the TS plane. A Carnot cycle appears as a square or rectangle when drawn in the TS plane. 

It is also apparent that isotherms, isobars, isochores, and adiabats should be termed perfect. Each presents a thermodynamic variable X for which /x = 0 and likewise for Qx- As would be expected, perfect pathways are admitted only by atypical circumstances. Perfect pathways can take a system from initial to final states only when these states happen to share identical X values. 

Define isobaric, isochoric, isenthalpic, and isothermal. Can a change in a gaseous system be isobaric, isochoric, and isothermal at the same time Why or why not ... 

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