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ch1 solutions - Chapter 1 Fundamental Concepts of...

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1-1 Chapter 1: Fundamental Concepts of Thermodynamics Problem numbers in italics indicate that the solution is included in the Student’s Solutions Manual. Questions on Concepts Q1.1) The location of the boundary between the system and the surroundings is a choice that must be made by the thermodynamicist. Consider a beaker of boiling water in an airtight room. Is the system open or closed if you place the boundary just outside the liquid water? Is the system open or closed if you place the boundary just inside the walls of the room? If the system boundaries are just outside of the liquid water, the system is open because water can escape from the top surface. The system is closed if the boundary is just inside the walls, because the room is airtight. Q1.2) Real walls are never totally adiabatic. Order the following walls in increasing order with respect to being diathermal: 1-cm-thick concrete, 1-cm-thick vacuum, 1-cm- thick copper, 1-cm-thick cork. 1-cm-thick vacuum < 1-cm-thick cork < 1-cm-thick concrete < 1-cm-thick copper Q1.3) Why is the possibility of exchange of matter or energy appropriate to the variable of interest a necessary condition for equilibrium between two systems? Equilibrium is a dynamic process in which the rates of two opposing processes are equal. However, if the rate in each direction is zero, no exchange is possible, and therefore the system can not reach equilibrium. Q1.4) At sufficiently high temperatures, the van der Waals equation has the form m RT P V b . Note that the attractive part of the potential has no influence in this expression. Justify this behavior using the potential energy diagram in Figure 1.6. At high temperatures, the energy of the molecule is large as indicated by the colored rectangular area in the figure below.
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Chapter 1/Fundamental Concepts of Thermodynamics 1-2 In this case, the well depth is a small fraction of the total energy. Therefore, the particle is unaffected by the attractive part of the potential. Q1.5) The parameter a in the van der Waals equation is greater for H 2 O than for He. What does this say about the form of the potential function in Figure 1.6 for the two gases? It says that the depth of the attractive potential is greater for H 2 O than for He. Problems P1.1 ) A sealed flask with a capacity of 1.00 dm 3 contains 5.00 g of ethane. The flask is so weak that it will burst if the pressure exceeds 1.00 × 10 6 Pa. At what temperature will the pressure of the gas exceed the bursting temperature? 6 3 3 1 1 1 1.00 10 Pa 10 m 723 K 5.00 g 8.314J mol K 30.07 g mol PV T nR × × = = = × × P1.2) Consider a gas mixture in a 2.00-dm 3 flask at 27.0ºC. For each of the following mixtures, calculate the partial pressure of each gas, the total pressure, and the composition of the mixture in mole percent.
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