Lecture_16 - Lecture 16 Internal energy For a system of a...

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Lecture 16 — Internal energy For a system of a single component, U must be a function of T, P (or T, v or P, v ), since there are only two independent state functions Expand the di ff erential of this state function, then, in T and v : dU = ( U/ T ) V dT + ( U/ V ) T dV Heat capacity. The first of these is C v , measured with calorimeter. Extensive or intensive, depend- ing on whether or not we made U intensive. Measurable, evidently, and a state function (since it’s the derivative of a state function). (How does a calorimeter work? Need a gadget for measuring temperature, and a calibrated source of heat. So we have dU = dQ , and we measure dT . Can calibrate a source of heat against a “mechanical work” source of heat.) If we have a constant-volume process, then, Δ U = T 2 T 1 C v ( T ) dT How does C v depend on T ? Molar heat capacity, C v /N ; how do liquids and gases compare? Liquids typically higher, because some of the heat energy is “stored” in disrupting the attractions between molecules. Example: compare C v /N for ideal gas and typical liquid.
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