Chapter Twelve Notes

Chapter Twelve Notes - Chapter 12 The Laws of...

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Chapter 12: The Laws of Thermodynamics I) Energy can be transferred to a system by heat and by work done on the system A) The work done on a gas at constant pressure (isobaric process) is :  1) W=-P Δ V 2) Work done by the gas on its environment is the negative of this B) The area under the graph in a PV diagram is equal in magnitude to the work done on the gas 1) If the arrow on the graph points towards larger volumes, the work done on the gas is negative 2) If the arrow on the graph points towards small volumes the work done on the gas is positive II) First law of thermodynamics: if a system undergoes a change from an initial state to a final state, where Q is the  energy transferred to the system by heat and W is the work done on the system, the change in internal energy of  the system  Δ U, is:  Δ U=Q+W A) Q is positive when energy is transferred into the system by heat B) Q is negative when energy is transferred out of the system by heat C) Internal energy of any isolated system must remain constant ( Δ U=0) D) Change in internal energy of an ideal gas is  Δ U=nC v Δ T III) Molar specific heat at constant volume of a monatomic gas, C v : is C v =3/2R A) Value depends on the gas and varies with temperature and pressure 1) Larger molar specific heat requires more energy to realize a given temperature change 2) Size depends on structure of the gas molecules and how many different ways it can store energy B) Degree of freedom: Each different way a gas molecule can store energy.  Contribute  ½  R to the molar  specific heat IV) Isobaric process: pressure remains constant as the gas expands or is compressed A) The temperature of an expanding gas must decrease as the internal energy decreases B) Q = nC p Δ 1) C P =5/2R  2) For ideal gases the molar heat capacity at constant pressure., C p  is the sum of the molar heat capacity  at constant volume C v  and the gas constant R: C P  = C V  + R V) Adiabatic process: no energy enters or leaves the system by heat A) System is insulated B) System is only thermally insulated not mechanically insulated (can still do work) C) Δ U=W because Q=0 D) Adiabatic index o the gas:  =C γ p /C v E) If a hot gas is allowed to expand so quickly that there is no time for energy to enter or leave the system by  heat, the work done on the gas is negative and the internal energy decreases b/c kinetic energy is  transferred from the gas molecules to the moving piston
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