161ASpring2010-Lecture9

# 161ASpring2010-Lecture9 - 1 Internal Energy of a Classical...

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1 “Classical” means Equipartition Principle applies: each molecule has average energy ½ kT per quadratic mode in thermal equilibrium. Internal Energy of a Classical ideal gas Internal Energy of a Classical ideal gas For an ideal gas, the internal energy only depends on the Temperature: U= ® NkT = ® nRT ( ® (often written f) depends on the type of molecule ) At room temperature, for most gases : monatomic gas (He, Ne, Ar, …) 3 translational modes (x, y, z) diatomic molecules (N 2 , O 2 , CO, …) 3 translational modes (x, y, z) + 2 rotational modes ( ϖ x , ϖ y ) non-linear molecules (H 2 O, NH 3 , …) 3 translational modes (x, y, z) + 3 rotational modes ( ϖ x , ϖ y , ϖ z ) T Nk 3 U = U= 3/2 NkT U= 5/2 NkT

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2 Internal energy of Real Gas A real gas has all the energy of the ideal gas plus the potential energy of interactions. r -3 -2 -1 0 1 2 3 4 1.5 2.0 2.5 3.0 3.5 4.0 distance van der Waals interaction U ( r )
3 Consider Two Systems Consider two identical systems shown to the right. In Case I , the gas is heated at constant volume ; in Case II, the gas is heated at constant pressure to the same higher temperature. heat q II heat q I

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Change in State at Constant Volume Substitute in 1) into 2) 1) 2) What is this at constant volume? What do each of these terms mean? How do we measure heat flow?
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161ASpring2010-Lecture9 - 1 Internal Energy of a Classical...

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