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# sect2 - ABE 201 Biological Thermodynamics 1 Ideal Gas...

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1 ABE 201 Biological Thermodynamics 1 Section 2 Ideal Gas Behavior ABE 201 Equations of State • Relates thermodynamic properties of a fluid (density, temperature, pressure, energetic state, etc.) • Simplest form is the Ideal Gas Law • Relate molar quantities and volumes of gases to temperature and pressure (PVT relationships) • (Charles and Boyle) PV = nRT What is specific volume ? 1 mole of ANY ideal gas at 0 ° C and 1atm occupies: 22.415 L 359 cubic feet The individual gas molecules have a negligible volume, thus any gas has the same volume overall, (the space between molecules is the primary component of the volume). Universal Gas Constant • R = in units of (pressure * volume)/(mole * temperature) • Pressure * Volume = Energy – Pa * m3 = (N/m 2 ) * m 3 = N-m = force * distance – R = energy/(mole*temperature) • Inside Back Cover of Text – 8.314 Pa-m 3 /(mol-K) – 10.73 psia-ft 3 /(lb-mol-R) – 8.314 J/(mol-K)

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2 Example • Given: A fire extinguisher holds 10 lb of CO 2 in a 20 ft 3 tank at 30 ° C, assuming the ideal gas law holds, calculate the gauge pressure on the tank. Ideal Gas Mixtures Suppose we have a mixture of gases A, B and C with specified volume and temp…. . Partial Pressure: pressure that would be exerted by n A moles of A alone in the same total volume V at the same temperature T. Partial Volume: the volume that would be occupied by n A moles of A alone at the total pressure P and temperature T of the mixture. Partial Pressure (noninteracting) + = Pa, V Pb, V Pa+Pb, V a only b only Same Volume Partial Pressures Partial Volume (noninteracting) + = P, Va P, Vb P, Va + Vb a only b only Same Pressure Partial Volumes
3 STP • Standard Temperature and Pressure • Basis for comparison between different gasses and gas flows System T P V N SI 273 K 1 atm 0.0224 m 3 1 mol CGS 273 K 1 atm 22.4 L 1 mol US 492K 1 atm 359.05 ft 3 1 mol Standard vs. Actual s s s s s s s T T n V ˆ P PV me) molar volu specific V ˆ ( RT V ˆ P nRT PV = = = = Example: • Oxygen flows into a reactor at 30 SCM per minute. Sensors at the inlet read 35 o C and 1500 kPa. What is the actual volumetric flow rate? Ideal Gas Mixtures If it is an ideal mixture each of the components does not interact with the others and therefore behaves ideally. PV = nRT p A V = n A RT p B V = n B RT p C V = n C RT etc….

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4 Ideal Gas Mixtures Dividing the partial ideal gas equation by the overall ideal gas expression we get: And therefore: Volume fraction: is the partial volume divided by the entire volume. This fraction multiplied by 100 gives the percentage by volume (% v/v) commonly referred to in problems. A A A y n n P p = = V y v P y p A A A A = = Partial Pressures can be Used to find mole fractions! Non Ideal Gas
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## This note was uploaded on 12/09/2011 for the course ABE 201 taught by Professor Nathanmosier during the Fall '11 term at Purdue.

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sect2 - ABE 201 Biological Thermodynamics 1 Ideal Gas...

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