SJSU Chem 9 - 1 Internal Energy of a Classical ideal gas...

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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 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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3 Heat Capacity at Constant Volume It takes more energy to increase the temperature of the same amount of material that has a higher heat capacity than one that has a lower heat capacity. Heat and Heat Capacity are both extensive properties. That is, they depend on the amount of material present. We therefore define Molar Heat Capacity = heat capacity per mole; C = C/N Specific Heat = heat capacity per gram; c = C/mass . The heat capacity at constant volume C V is defined as: For an ideal gas,
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4 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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This note was uploaded on 09/08/2010 for the course CHEM 160 at San Jose State University .

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SJSU Chem 9 - 1 Internal Energy of a Classical ideal gas...

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