l03 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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20 .110/5.60 Fall 2005 Lecture #3 page 1 EXPANSIONS, ENERGY, ENTHALPY Isothermal Gas Expansion (0 T ) = gas ( p 1 , V 1 , ) = gas ( 2 , 2 , ) Irreversibly (many ways possible) (1) Set ext = 0 p =0 T p 11 ,V p T p 22 ,V 2 1 (1) 0 v ext wp d = −= (2) Set ext = 2 T p ,V p 2 p 2 T p ,V () 2 1 2 (2) 1 =− - w (2) p p 2 p 1 V 1 V 2 Note, work is negative: system expands against surroundings 20.110J / 2.772J / 5.601J Thermodynamics of Biomolecular Systems Instructors: Linda G. Griffith, Kimberly Hamad-Schifferli, Moungi G. Bawendi, Robert W. Field
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20 .110/5.60 Fall 2005 Lecture #3 page 2 (3) Carry out change in two steps gas ( p 1 , V 1 , T ) = gas ( 3 , 3 , ) = gas ( 2 , 2 , ) 1 > 3 > 2 T p 11 ,V p 3 p 2 p 22 ,V p 3 T p 33 ,V T ( ) () 32 13 3 3 3 1 (3) vv VV wpd d −− =− = ∫∫ More work delivered to surroundings in this case. - w (3) p p 2 p 1 p 3 V 1 V 2 V 3 (4) Reversible change = ext throughout 2 1 rev wp - p p 2 p 1 V 1 V 2 Maximum work delivered to surroundings for isothermal gas expansion is obtained using a reversible path For ideal gas: = 2 1 ln ln Vp nRT wdV n R 20.110J / 2.772J / 5.601J Thermodynamics of Biomolecular Systems Instructors: Linda G. Griffith, Kimberly Hamad-Schifferli, Moungi G. Bawendi, Robert W. Field
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20 .110/5.60 Fall 2005 Lecture #3 page 3 The Internal Energy U dU = q + w (First Law) d - d - ext path dU C dT p dV =− And () , VT UU UTV TV ⎛⎞ ⎜⎟ ⎝⎠ ∂∂ ⇒= + Some frequent constraints: Reversible q rev + = rev – pdV ( ) = d - d - d - Isolated q = w = 0 d - d - Adiabatic q = 0 w -pdV reversible d - d - Constant V V d - T
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l03 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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