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AP Physics II.C

AP Physics II.C. Kinetic Theory and Thermodynamics. The Ideal Gas Law. An ideal gas – one of low density (i.e. particles are far enough apart they have few interactions), low pressure (a little less than 1 atm.) and a temperature that is not near the boiling point for that gas.

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AP Physics II.C

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  1. AP Physics II.C Kinetic Theory and Thermodynamics

  2. The Ideal Gas Law

  3. An ideal gas – one of low density (i.e. particles are far enough apart they have few interactions), low pressure (a little less than 1 atm.) and a temperature that is not near the boiling point for that gas.

  4. Three Relationships for Gasses • Pressure and volume (Boyle’s Law) • Volume and temperature (Charles’ Law) • Pressure and temperature (Gay-Lussac’s Laws)

  5. So, an ideal gas is one that obeys this relationship between pressure, volume and temperature. PV = nRTis known as the Ideal Gas Law. R is the universal gas constant (8.315 J/mol·K), n is the number of moles and temperature is given in Kelvin.

  6. Avagadro’s constant and moles (the gram equivalent of the particle’s atomic or molecular mass) • One mole of carbon-12 = ? • One mole of CO2 = ? • One mole of water = ? • One mole of oxygen = ?

  7. Ex. A 0.10 mole sample of gas is confined to a jar whose volume if 4.0 L. What is the temperature of the gas if the pressure is 2.0 atm?

  8. Pre-AP: Time out to talk about pressure

  9. Ex. A cylindrical container of radius 15 cm and height 30 cm contains 0.6 mole of a gas at 433 K. How much force does the confined gas exert on the lid of the container?

  10. 14.3 Kinetic Theory of Gasses

  11. The concept that gasses are composed of atoms in continuous random motion is called the Kinetic Theory of Gasses.

  12. So . . . What we’ve found is the average kinetic energy of gas molecules is directly proportional to their absolute temperature

  13. Ex. A tank contains two 2.0 mol of He gas at 20.0º C. Find the average kinetic energy per molecule and the average speed of of the molecule.

  14. Ex. By how much must the temperature of a sample of gas increase to triple the average speed of the molecules?

  15. Internal Energy of a Monatomic Ideal Gas

  16. Thermodynamics – the branch of physics which studies laws relating heat and work

  17. Closed system (mostly what we are concerned with) – one in which no mass enters or leaves (but energy may be exchanged with the environment)

  18. State of the system – described by giving values for pressure, volume, temperature and mass.

  19. First Law of Thermodynamics

  20. The internal energy of a system can change due to • An addition or loss of heat (Q is positive if the system gains heat; Q is negative is the system loses heat) • Work done on or by the system (work is positive if work is done on the system; work is negative if work is done by the system – this ain’t what your book says)

  21. The First Law of Thermodynamics as an equation(a statement of conservation of energy) ΔU = Q + W

  22. Ex. 2500 J of heat are added to a system and 1800 J of work is done on the system. What is the change in internal energy? What is the change in internal energy if 1800 J of work is done by the system?

  23. Thermal Processes

  24. The process occurs slowly enough that uniform pressure exists throughout all regions of the system at all times.

  25. 1. Isobaric (constant pressure) – basically a way to derive a formula

  26. PV diagram for isobaric process (what is the area under the curve?)

  27. 2. Isothermal Process (constant temperature)

  28. An expanding balloon

  29. PV diagram for isothermal process

  30. Calculating work for an isothermal process

  31. An isothermal process and the First Law

  32. 3. Adiabatic – no heat flows in or out of the system (Q is constant) Examples: bicycle pump, diesel engine, stretching a rubber band, compressed gas released from a container

  33. PV diagram

  34. Calculating work – another non-boxer. Work is estimated from the area under the curve as it is for any PV diagram.

  35. An adiabatic process and the First Law

  36. Note: two adiabatic processes are always connected by two isotherms (a Carnot engine – more on this later)

  37. 4. Isovolumetric (isochoric) – constant volume

  38. An isovolumetric process and the First Law

  39. PV diagram for an isochoric process

  40. The First Law and an Isochoric Process

  41. Ex. What is the work done on/by the gas for each process shown in the PV diagram? Is work done on or by the gas in each process? What is the net work done for the cycle? Is the net work done on or by the gas?

  42. Ex. A 0.5 mol sample of an ideal gas is brought from state a to state b when 7500 J of energy is added along the path shown in the PV diagram. Find a) the temperature at a b) the temperature at b c) the work done by the gas during the process ab and d) the change in internal energy of the gas.

  43. Ex. A 0.5 mol sample of an ideal monatomic gas is brought from state a to state b along the path shown in the following PV diagram. a) What is the work done by the gas during these three process? b) What is the change in internal energy of the gas for these three processes? c) What is the net heat added during theses three processes?

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