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First_Law_relations - Closed System 1 mv2 mgz QIN WIN QOUT...

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Closed System ( 29 ( 29 ( 29 ( 29 + - = ∆ + + - - = - + + v v v 2 IN IN OUT OUT c c CM 2 2 2 1 2 1 2 1 c c Energy crossing the boundary = change in closed system energy 1 m mgz Q W Q +W U 2 g g g z 1 ( ) 2 g g CM CM z m u u Open System In Rate Form = = + + + + - + + + = v v 2 N i i IN IN IN,i i i 1 c c 2 M j j CV j OUT OUT OUT,j j 1 c c gz Q W m (h ) 2g g gz dE Q +W m (h ) 2g g dt & & & & & & Integrated between time t 1 (State 1) and time t 2 (State 2) = = + + + + - + + + = - v v 2 2 N M j j i i IN IN IN,i i j OUT OUT OUT,j i 1 j 1 c c c c 2 1 CV CV ( Energy crossing the boundary (work, heat transfer, carried by mass))
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