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heatcapacitycalculations

# heatcapacitycalculations - Department of Chemical...

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Department of Chemical Engineering University of California, Santa Barbara ChE 110A Heat capacities in enthalpy and entropy calculations Enthalpy calculations Consider adding a fixed amount of heat g to a closed system initially at temperature G ± , at constant pressure. We would like to know the final temperature G ² . Applying the first law, we find that: ³´ µ ¶ ·g ¸ ·¹ ¶ ·g º »³¼ µ We can rearrange this equation: ·g ¶ ½³´ ¸ ½»³¼ Substituting ´ ¶ ¾ º »¼ : ·g ¶ ½¿³¾ º »³¼ º ¼³»À ¸ ½»³¼ ¶ ½³¾ º ½¼³» Since the pressure is constant, ³» ¶ 0 and this expression simplifies so we can integrate: ·g ¶ ½³¾ g ¶ ½Δ¾ By definition, Á Â Ã Ä ÅÆ ÅÇ È Â , and so we can write: g ¶ ½ É Á Â Ç Ê Ç Ë ³G If the heat capacity is constant, we find that g ¶ ½Á Â ÌG ² º G ± Í . On the other hand, in general the heat capacity can be temperature-dependent. A general temperature-dependent empirical form for the heat capacity for ideal gases and incompressible liquids is: Á Â Î ¶ Ï ¸ ÐG ¸ ÁG ² ¸ ÑG Ò² where Ï, Ð, Á, and Ñ are substance-dependent constants and G is absolute temperature. Substituting this into the enthalpy integral and performing the integration, we arrive at:

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heatcapacitycalculations - Department of Chemical...

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