6-The 1st law calculation of ideal gases

# 6-The 1st law calculation of ideal gases - BioE The first...

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Molecular BioEngineering Laboratory BioE The first Law calculation of ideal gases ± Internal energy of ideal gases ± C V and C p ± Calculation of Δ U, W and Q of ideal gases

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BioE Internal energy of an ideal gas ± U = U(V,T) = U(P,T) = U(P,V) = z Kinetic Energy temperature z Potential Energy volume ± Internal energy of an ideal gas is a function of T only. U = U(T) z Ideal gas has no actual volume. z There is no molecular interaction between ideal gases.
BioE Joule s experiment 理想氣體 真空 T 1 T 2 T 1 = T 2

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BioE Analysis of Joule s experiment ± System: ideal gas ± It was found that the temperature of the bath remained constant. It means that there was no heat interaction between system and environment, that is, Q = 0. ± There was no work done on the environment during the whole process, therefore, W = 0. ± According to the first law of thermodynamics, Δ U = Q - W, we know that Δ U = 0. ± dU = 0, dT = 0 but dV 0, therefore, U is not a function of V for an ideal gas. ± Internal energy of an ideal gas is a function of temperature only.
BioE Calculation of Δ U = Δ = = = 2 1 ) ( , 0 T T V ig ig ig V ig ig T ig dT T U U T U U dT T U dU V U Q Ideal gas dV V U dT T U dU T V U U T V + = = ) , (

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BioE How to measure internal energy and enthalpy? 0 if = = Δ = = Δ dV Q U dV P Q W Q U V ext Q V Q P 0 if = Δ = Δ + Δ = Δ Δ + Δ + Δ = Δ + P Q V P U H P V V P U H PV U H P 定壓加熱 定容加熱
BioE Heat capacity ± 系統溫度每升高 1 度所需 吸收的熱量 ± C V ：定容加熱系統所測得 之熱容量 ± C P ：定壓加熱系統所測得 之熱容量 = = dT dU T U T Q C ig V V ig V δ = = dT dH T H T Q C ig p p ig p

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BioE
BioE

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BioE 雙原子分子的移動動能 ± Translational kinetic energy contributes z 3 x 1/2 RT to total internal energy (a) 移動
BioE ± Rotational kinetic energy contributes z 2 x 1/2 RT to total internal energy of a linear molecule z 3 x 1/2 RT to total internal energy of a nonlinear molecule 雙原子分子的轉動動能

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BioE 雙原子分子的振動動能 ± Vibrational kinetic energy may contribute z (3m–3–2)RT to total internal energy of a linear molecule z (3m–3–3)RT to total internal energy of a nonlinear molecule * m is the number of atoms in a molecule (c) 振動
BioE Maximum internal energy increase from

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6-The 1st law calculation of ideal gases - BioE The first...

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