Thermodynamics Notes5

Thermodynamics Notes5 - ME 311 FALL 2007 CHAPTER 2...

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ME 311 THERMODYNAMICS S. Masutani FALL 2007 1 CHAPTER 2 (continued) Reiterating The energy (E = U + KE + PE) of a closed system is altered by interactions between the system and its surroundings. These interactions are divided into work and heat transfer. We indicate this by: Production = 0 = (outflow – inflow)* + storage *for closed system: due to work or heat transfer storage = Δ E E 2 – E 1 = (inflow – outflow)* \_____________/ Q – W (using the textbook’s sign convention for W and Q) For an adiabatic process from initial state 1 to final state 2, Δ E = -W adiabatic For example: consider a well-insulated vessel Æ assume adiabatic Work performed by stirrer can be determined if we can find means to identify the change in energy of the system, Δ E. However, if the insulation is removed, then Δ E –W (non-adiabatic) The difference between | Δ E| and |W| arises from energy exchange between the system and environment via heat transfer. . Sign convention for hest transfer, Q Textbook: Q > 0: heat transfer to system from environment. Q < 0: heat transfer from system to environment
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ME 311 THERMODYNAMICS S. Masutani FALL 2007 Alternative : Indicate (select) direction of +Q by means of the direction of an arrow in a sketch of the system. If results of your analysis indicate a negative value of Q Æ direction opposite of the one selected (i.e., shown in the sketch). Note that the sign convention is not critical as long as it is properly defined and the 1 st Law, which can be stated as: Production of energy = 0 = outflow of energy – inflow of energy + storage of energy or Storage of energy in the system = inflow of energy to system – outflow of energy from system is applied in accordance with this definition. For example, the sign convention employed in the textbook is: +W +Q E and the corresponding energy balance is; Δ E = Q – W If we reverse the sign convention as shown below: 2 +W +Q E Then the energy balance should be expressed as: Δ E = W – Q The important point here is that the W’s and Q’s are placed in the appropriate “bins,” i.e., either outflows or inflows, in the energy accounting equation. As an example, consider a system with multiple work and heat transfer interactions with its surroundings:
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ME 311 THERMODYNAMICS S. Masutani FALL 2007 E Q 1 Q 2 W 2 W 1 If we adopt the textbook’s sign convention so that W is positive when it is done by the system on the surroundings (outflow) and Q is positive from the surroundings into the system (inflow), then Δ E = Q – W But one needs to be careful to note that = i i Q Q which, for this example, and in accordance with our selected sign convention, is: Q = Q 1 + (-Q 2 ) = Q 1 - Q 2 Similarly, = i i W W = (-W 1 ) + W 2 = W 2 – W 1 Hence, the energy balance is: Δ E = Q – W = (Q 1 - Q 2 ) – (W 2 – W 1 ) = (Q 1 + W 1 ) – (Q 2
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Thermodynamics Notes5 - ME 311 FALL 2007 CHAPTER 2...

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