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CH E 312 Lecture 12 - We learned 5.2.2 The first law of...

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CV 𝒎𝒎 𝒊𝒊𝒊𝒊 ̇ = 𝝆𝝆 𝟏𝟏 𝑽𝑽 𝟏𝟏 𝑨𝑨 𝟏𝟏 𝒎𝒎 𝒐𝒐𝒐𝒐𝒐𝒐 ̇ = 𝝆𝝆 𝟐𝟐 𝑽𝑽 𝟐𝟐 𝑨𝑨 𝟐𝟐 𝑾𝑾 ̇ 𝑪𝑪𝑽𝑽 𝑸𝑸 ̇ 𝑪𝑪𝑽𝑽 𝒎𝒎 𝒊𝒊𝒊𝒊 ̇ 𝒆𝒆 𝟏𝟏 𝒎𝒎 𝒐𝒐𝒐𝒐𝒐𝒐 ̇ 𝒆𝒆 𝟐𝟐 𝒎𝒎 𝒊𝒊𝒊𝒊 ̇ 𝑷𝑷 𝟏𝟏 𝝆𝝆 𝟏𝟏 𝒎𝒎 𝒐𝒐𝒐𝒐𝒐𝒐 ̇ 𝑷𝑷 𝟐𝟐 𝝆𝝆 𝟐𝟐 mass flow rate coming to the CV: energy added to the CV through incoming mass flow rate: energy added to the CV through the work of the incoming mass flow rate: 5.2.2. The first law of thermodynamic for CV: We learned…. E cv 1 2
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5.2.2. The first law of thermodynamic for CV: 2 𝜕𝜕 ∫ 𝜌𝜌 ( 𝑢𝑢 + 1 2 𝑉𝑉 2 + 𝑔𝑔𝑔𝑔 ) 𝑑𝑑∀ 𝑐𝑐𝑣𝑣 𝜕𝜕𝜕𝜕 = � 𝜌𝜌𝑉𝑉 𝑛𝑛 𝑎𝑎𝑎𝑎𝑎𝑎 𝑖𝑖𝑛𝑛 𝐴𝐴 𝑃𝑃 𝜌𝜌 + 𝑢𝑢 + 1 2 𝑉𝑉 2 + 𝑔𝑔𝑔𝑔 − � 𝜌𝜌𝑉𝑉 𝑛𝑛 𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜𝑜𝑜 𝐴𝐴 𝑃𝑃 𝜌𝜌 + 𝑢𝑢 + 1 2 𝑉𝑉 2 + 𝑔𝑔𝑔𝑔 + 𝑄𝑄 𝑛𝑛𝑛𝑛𝑜𝑜 ̇ + 𝑊𝑊 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑜𝑜 ̇ Eq. 5-2 Example The rate of change of the energy in CV = The rate of energy transfer due to mass transfer to or from CV The rate of energy transfer due to work and heat transfer to or from CV + We learned….
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3 𝜕𝜕 ∫ 𝜌𝜌 ( 𝑢𝑢 + 1 2 𝑉𝑉 2 + 𝑔𝑔𝑔𝑔 ) 𝑑𝑑∀ 𝑐𝑐𝑣𝑣 𝜕𝜕𝜕𝜕 = � 𝜌𝜌𝑉𝑉 𝑛𝑛 𝑎𝑎𝑎𝑎𝑎𝑎 𝑖𝑖𝑛𝑛 𝐴𝐴
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