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Unformatted text preview: Physical Chemistry (I) Quiz 02 Oct. 11, 2007 1. (30%) The change of pressure ( Δ P ) of a liquid with increasing temperature can be estimated if one knows the volumetric thermal expansion coefficients [ 1 ( ) P V V T ∂ = ∂ β ] and the isothermal compressibility [ 1 ( ) T V V P ∂ = - ∂ κ ] of the system. (a) Assuming P = P ( T , V ), using the mathematics of partial derivatives to derive d P in terms of β and κ . (5%) (b) Using the chain rule for differentiation, show that the isobaric expansion coefficient expressed in terms of density is given by 1 . P T ρ β ρ ∂ = - ∂ (5%) (c) Because V is a state function and d V is an exact differential, show that the isothermal compressibility and isobaric expansion coefficient are related by . T P P T β κ ∂ ∂ = - ∂ ∂ (5%) (d) A vessel is filled completely with liquid water and sealed at 25.0ºC and a pressure of 1.00 bar. What is the pressure if the temperature of the system is raised to 60.0ºC? Assuming β water = 2.04 × 10 –4 K –1 , β vessel = 1.02 × 10 –4 K –1 , and κ water = 4.59 × 10 –5 bar –1 . (15%) 2. (25%) The total differential of the internal energy can be written as V V T V U U P dU dT dV C dT T P dV T V T ∂ ∂ ∂ = + = +- ∂ ∂ ∂ . (a) Express the internal pressure T U V ∂ ∂ in terms of P , β , T , and κ . (5%) (b) Determine the value of T U V ∂ ∂ for an ideal gas. (5%) (c) Derive Joule coefficient ( μ J ) in relation to T U V ∂ ∂ and C V . (5%) (d) Derive the following expression for calculating the isothermal change in the constant volume heat capacity: 2 2 . V T V C P T V T ∂ ∂ = ∂ ∂ (10%) 3. (25%) The total differential of the enthalpy can be written as P V T P H H V dH dT dP C dT V T dP T P T ∂ ∂ ∂ = + = +- ∂ ∂ ∂ ...
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