PS5 - accompanying expansion and contraction of the metal...

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ChemE 3130 – Chemical Engineering Thermodynamics – Problem Set #5 (1) MDK 4.8 (2) MDK 4.18 [Hint: Assume that the potential energy between two molecules depends on the amount of time that they spend close to each other, then it would be inversely related to velocity. Use arguments from statistical mechanics to describe the basis for the T -1/2 term. (3) MDK 4.29 (4) MDK 4.30 b,d,e (5) Over a limited range of conditions, a fluid has an isothermal compressibility κ T ( ) = - 1 V V P ae è ç ö ø ÷ T = q + f T and a coefficient of thermal expansion β P ( ) = 1 V V T ae è ç ö ø ÷ P = h + xP , where θ , f , h , andx are constants. Find the equation of state these relationships imply. (6) The expansion and contraction of metal upon heating and cooling may be used to create a thermal heat engine. In Fig. 1, heat is added to the top of a cylinder through radiation, and lost via the same process at the bottom. The
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Unformatted text preview: accompanying expansion and contraction of the metal causes the cylinder to rotate by creating a net torque. Work may be harnessed from this rotation. By Taylor expansion one may show the stress of the cylinder in the x direction is given by: d ( , 29 = ( , 29 + 1 (-29 + 2 (-29 , where x , L ,and T , are the normal stress in the x direction, the average length, and the average temperature of the cylinder respectively. Let a 1 and a 2 be constants. Draw an idealized x vs. L diagram (analogous to a PV diagram for a gas) for the cycle (that is, a full rotation). What would the actual diagram look like qualitatively (sketch this on your previous diagram and explain your answer). ChemE 3130 Chemical Engineering Thermodynamics Problem Set #5...
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PS5 - accompanying expansion and contraction of the metal...

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