3. So-called permanent diatomic gases, namely H2, O2, N2, Air, NO, and Co (a) Cy(or Cv) is nearly constant at ordinary temperatures, being approximately (5/2)R [(5/2R for one kmol], and increases slowly at higher temperatures (b) cp(or Cp )is nearly constant at ordinary temperatures, being approximately (7/2)R [(7/2)R for one kmol], and increases slowly at higher temperatures (c) y is constant over a temperature range of roughly 150 to 600K and is very nearly equal to 775 Ly=1. 4]. It decreases with temperature above this 4. Polyatomic gases and gases that are chemically active, such as CO2, NH3, CH4, and Freons: The specific heats, cv and cp, and vary with the temperature, the variation being different for each gas. The general trend is that heavy molecular weight gases (i.e, more complex gas molecules than those listed in 2 or 3), have values of closer to unity than diatomic gases, which, as can be seen above, are closer to unity than monatomic gases. For example, values of y below 1. 2 are typical of Freons which have molecular weights of over one hundred Adapted from Zemansky, M. w. and Dittman, R.H., Heat and Thermodynamics", Sixth Edition, McGraw-Hill book company, 1981 16) Reversible adiabatic processes for an ideal From the first law, with 0=0, du CudT, and Work= Pd du t pdv=0 () Also, using the definition of enthalpy dh= du+ pdy vdP The underlined terms are zero for an adiabatic process. Re-writing(i) and (ii) ydT=-yPdv dt= vdP Combining the above two equations we obtain - y Pdv= vdP or -y dv/v= dP/P Equation(iii) can be integrated between states I and 2 to give yIn(v2/)=In(P2/Pn), or, equivalently, (P2)PYi )=1 For an ideal gas undergoing a reversible, adiabatic process, the relation between pressure and olume is thus P=constant xp I7 Examples of flow problems and the use of enthalpy a) Adiabatic, steady, throttling of a gas(flow through a valve or other restriction) Figure 0-l shows the configuration of interest. We wish to know the relation between properties upstream of the valve, denoted by l"and those downstream, denoted by 2 0-90-9 3. So-called permanent diatomic gases, namely H2, O2, N2, Air, NO, and CO: (a) cv (or CV ) is nearly constant at ordinary temperatures, being approximately (5/2)R [(5/2)R , for one kmol], and increases slowly at higher temperatures. (b) cp (or CP ) is nearly constant at ordinary temperatures, being approximately (7/2)R [(7/2)R , for one kmol], and increases slowly at higher temperatures. (c) γ is constant over a temperature range of roughly 150 to 600K and is very nearly equal to 7/5 [γ = 1.4]. It decreases with temperature above this. 4. Polyatomic gases and gases that are chemically active, such as CO2, NH3, CH4, and Freons: The specific heats, cv and cp, and γ vary with the temperature, the variation being different for each gas. The general trend is that heavy molecular weight gases (i.e., more complex gas molecules than those listed in 2 or 3), have values of γ closer to unity than diatomic gases, which, as can be seen above, are closer to unity than monatomic gases. For example, values of γ below 1.2 are typical of Freons which have molecular weights of over one hundred. Adapted from Zemansky, M. W. and Dittman, R. H., "Heat and Thermodynamics", Sixth Edition, McGraw-Hill book company, 1981 16) Reversible adiabatic processes for an ideal gas From the first law, with Q = 0, du = cvdT, and Work = Pdv du + Pdv = 0 (i) Also, using the definition of enthalpy dh = du + Pdv + vdP. (ii) The underlined terms are zero for an adiabatic process. Re-writing (i) and (ii), γ cvdT = - γ pdT = vdP. Pdv c Combining the above two equations we obtain -γ Pdv = vdP or -γ dv/v = dP/P (iii) Equation (iii) can be integrated between states 1 and 2 to give γln(v2/v1) = ln(P2/P1), or, equivalently, ( )( ) / 1 2 2 1 1 = γ γ P v Pv For an ideal gas undergoing a reversible, adiabatic process, the relation between pressure and volume is thus: Pvγ = constant, or P = constant ×ργ . 17) Examples of flow problems and the use of enthalpy a) Adiabatic, steady, throttling of a gas (flow through a valve or other restriction) Figure 0-1 shows the configuration of interest. We wish to know the relation between properties upstream of the valve, denoted by “1” and those downstream, denoted by “2