Example 7-7
Aluminum at 100oC is placed in a large, insulated tank having 10 kg of water at a temperature of 30oC. If the mass of the aluminum is 0.5 kg, find the final equilibrium temperature of the aluminum and water, the entropy change of the aluminum and the water, and the total entropy change of the universe because of this process. Before we work the problem, what do you think the answers ought to be? Are entropy changes going to be positive or negative? What about the entropy generated as the process takes place?
System: Closed system including the aluminum and water.
Property Relation: ?
Process: Constant volume, adiabatic, no work energy exchange between the aluminum and water.
Conservation Principles:
Apply the first law, closed system to the aluminum-water system.
Using the solid and incompressible liquid relations, we have
But at equilibrium, T2,AL = T2,water = T2
The second law gives the entropy production, or total entropy change of the universe, as
Using the entropy change equation for solids and liquids,
Why is Sgen or STotal positive?