solutions 1

solutions 1 - PHYS 253 Assignment 1 Problem 1 a Taking the...

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Unformatted text preview: PHYS 253: Assignment 1 Problem 1 a. Taking the derivative of both sides of the equation of state (EOS) with respect to v , at constant T : ∂ ∂v T p + a v 2 ( v- b ) = 0 ( v- b ) ∂p ∂v T- 2 a v 3 + p + a v 2 , = 0 ∂p ∂v T = 2 a v 3- RT ( v- b ) 2 b. Taking the derivative with respect to T , at constant v : ( v- b ) ∂ ∂T v p + a v 2 = R ∂p ∂T v = R v- b c. We can do this directly by taking the derivative with respect to T , at constant p , or we can use the results from parts a and b along with equations 2.5 and 2.6 from the textbook: ∂p ∂v T ∂v ∂T p ∂T ∂p v =- 1 ∂T ∂p v = 1 ( ∂p/∂T ) v Now we can write ∂v ∂T p =- ∂p ∂T v ∂p ∂v T =- R/ ( v- b ) 2 a v 3- P + a/v 2 v- b ∂v ∂T p = R ( P + a/v 2 )- 2 a ( v- b ) v 3 Problem 2 Taking ( ∂/∂T ) p of both sides of the EOS: r p- a ∂ ∂T ( T- m ) = ∂v ∂T p r p + am T m +1 = ∂v ∂T p β = 1 v ∂v ∂T p = r p + am T m +1 rT p- a T m + b – 2 – Problem 3 a. Using equation 2.7 from the textbook, for constant volume:a....
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This note was uploaded on 12/15/2010 for the course PHYS 253 taught by Professor Petergrutter during the Fall '10 term at McGill.

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solutions 1 - PHYS 253 Assignment 1 Problem 1 a Taking the...

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