hw3_solutions_F

# hw3_solutions_F - CH353M Homework assignment 3(due Friday...

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CH353M Homework assignment 3 ( due Friday Oct. 14 ) 1. ( 5 ) Derive the expression for pv C-C for a material with the following equation of state: 2 Va b P c T =+ + , where a , b , and c are constants. 2 2 2 2 PV V P P V cT cT CCT TT b V ba b P c T  ∂∂ −= = =  ++  2 (20). One mole of a gas occupies one half of a container that is separated from the rest of the container by a partition. The initial volume of the gas is V and its temperature is T . After the partition is removed, the gas expands irreversibly and occupies the volume 2 V . The equation of state of the gas is 2 (/ ) ( ) PaV Vb R T +− = and its heat capacity V C is temperature-independent. A. What is the temperature of the gas after expansion? We have dU = V C n dT + [T V P T -P] dV Using P = RT/(V-b) – a/V 2 we find 22 VV RT RT a dV dU C dT dV C dT a VbVbV V =+ −+ −− Integrating this, 11 (( 2 ) ( 1 ) ) 0 (2) (1) V UCT T a ∆= = or, using V(2)=2V(1)=2V,

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T(2)=T(1)- 2 V a CV B. What is the change of the entropy of the gas in this process? Use VV V CC PR d V dS dV dT dT TT V b T  =+ = +  ∂−  S=R ln((2V-b)/(V-b)) + /(2 ) ln V V Ta C V C T C. In the class, we have derived the relationship () / constant CRC PV + = between the pressure and the volume of an ideal gas undergoing a reversible adiabatic process, in which it receives no heat from the surroundings. Derive an analogous
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hw3_solutions_F - CH353M Homework assignment 3(due Friday...

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