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State Postulate

State Postulate. According to the State Postulate the number of intensive variable needed to specify all other intensive variables equals the number of relevant, reversible work modes plus one.

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State Postulate

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  1. State Postulate According to the State Postulate the number of intensive variable needed to specify all other intensive variables equals the number of relevant, reversible work modes plus one. Here there is one such mode (mechanical compression); i.e., two intensive variables define the system.

  2. Equations of State • If there are other work modes (electrical or magnetic forces) we need one additional variable per mode. • It requires one additional variable, which must be extensive to determine all other extensive variables. • Use equations of state to determine unknown variables from those known.

  3. Thermally Perfect Gases A thermally perfect gas is one whose molecules have negligible volume and do not interact with each other. pV = nRT p = cRT pV = mRT p = RT

  4. Compressibility • Compressibility Z is defined as: Perfect Gas Z = 1 Imperfect Gas Z < 1 Gases are not thermally perfect at higher pressures. For a perfect gas it can also be shown that U = U(T only)

  5. Properties of a Gas In general let’s say u = u(T,V), then For a thermally perfect gas:

  6. Specific Heat • The specific heat is the amount of heat required to raise the substance by one degree. • Since heat is not a state variable, path must be specified. • For gases we use cv and cp. • Not valid at phase change, with work.

  7. Relationship between cv & cp In general: For perfect gas: If cv & cp constant, gas calorically perfect If thermally and calorically perfect, gas is ideal

  8. Enthalpy The expression u + pV occurs frequently Define the enthalpy as : h = u + pV Since for a perfect gas pV = RT h = h(T only)

  9. Properties of a Gas In general let’s say h = h(T,p), then For a thermally perfect gas:

  10. Relationship between cv & cp In general: For perfect gas:

  11. Ratio of Specific Heats Definition: For perfect gas: Also: 1 <  < 1.67, for air  = 1.4

  12. Incompressible Substances • Liquids or solids (e.g., water  =0.1 % for a change from 1 atm. to 50 atm.) Generally If incompressible v-constant then

  13. Incompressible Substances Now: dh = du + d(pv) = du + pdV =Vdp dh = cvdT +Vdp Compare with: h = h(t,p) then Compare dT terms: cp = cv = c Only one value of specific heat

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