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Understanding Isothermal Processes in Gas Compression

Explore the concepts behind isothermal processes in gas compression. Discover how gases can be compressed without temperature increase and compare molar heat capacities for constant volume and pressure changes. Quiz questions and demos included.

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Understanding Isothermal Processes in Gas Compression

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  1. Announcements 1/26/11 • Prayer • Please do this “Quick Writing” assignment while you’re waiting for class to start: Ralph is confused because he knows that when you compress gases, they tend to heat up (think of a bicycle pump nozzle getting hotter as you force the gas from the pump to the tire). So, how are “isothermal” processes possible? How can you compress a gas without its temperature increasing?

  2. Demo • Constant volume change, aka “alcohol rocket”

  3. Thought question • How will the temperature of the gas change during this process from A to B? • Increase • Decrease • First increase, then decrease • First decrease, then increase • Stay the same

  4. Reading quiz • What is “CV”? • heat capacity • mass-pacity • molar heat capacity • molar heat capacity, but only for constant volume changes • your “curriculum vitae”, a detailed resumé

  5. Thought question • Which will be larger, the molar heat capacity for constant volume changes or the molar heat capacity for constant pressure changes? (Hint: Think of the First Law.) • constant volume • constant pressure • they are the same • it depends on the temperature

  6. CV and CP • Constant volume change (monatomic): W = 0 Eint = Qadded (3/2)nRT = Qadded Compare to definition of C: Qadded = nCVDT CV = (3/2)R (monatomic) • Constant pressure change • What’s different? • result: CP = (5/2)R (monatomic) • What would be different for gases with more degrees of freedom?

  7. Reading quiz (graded) • What does gamma equal in the equation for an adiabatic process: • CP + CV • CP - CV • CV - CP • CV / CP • CP / CV

  8. Isothermal vs Adiabatic • Isothermal: • Adiabatic:  steeper curves for adiabatic

  9. Thought question • How much do you think the temperature of the air in this room would change by if I compressed it adiabatically by a factor of 10? (Vf = V0/10) • less than 0.1 degree C • about 0.1 degrees C • about 1 degree C • about 10 degrees C • more than 10 degrees C

  10. Demo/Video • Demo: freeze spray • Video: adiabatic expansion • Demo: adiabatic cotton burner

  11. Derivation of PVg (for Monatomic) Eint = Qadded + Won (3/2) nRT = - PdV (3/2) nRdT = -PdV (3/2) nR d(PV/nR) = -PdV (3/2) (PdV + VdP) = -PdV (3/2) VdP = -(5/2) PdV dP/P = -(5/3) dV/V lnP = (-5/3)lnV + constant lnP = ln(V-5/3) + constant P = constant  V-5/3 (it’s a different constant) P V5/3 = constant What’s different if diatomic?

  12. Thought question • Which of the curves on the PV diagram below is most likely to represent an isothermal compression, followed by an adiabatic expansion back to the initial volume?

  13. Thought questions • What would be the molar specific heat for an adiabatic process? (Hint: think of Q = nCDT.) • CV • CV + R • CV + 2R • CV - R • none of the above • What would be the molar specific heat for an isothermal process? (Same hint.) • CV • CV + R • CV + 2R • CV - R • none of the above

  14. Water/steam “saturation curve”: ideal gas?

  15. Water/steam “saturation curve”: ideal gas?

  16. Water/steam “saturation curve”: ideal gas?

  17. Water/steam “saturation curve”: ideal gas?

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