Plumber's solder is composed of 67% lead and 33% tin by weight. Describe what happens to this mixture as it cools, and explain why this composition might be more suitable than the eutectic composition for joining pipes.
As a result, the tin and lead mixture is better for joining pipes.
Plumber's solder is composed of 67% lead and 33% tin by weight.
Take a look at the phase diagram for a tin-lead mixture in the graph below. By weight, the solder combination contains 67 percent lead and 23 percent tin. If the mixture cools, the temperature will drop from the dashed red line on the graph until it hits the temperature boundary between the liquid phase and the solid Pb-Liquid phase, which is 250 K, and the lead will begin to freeze. The remaining liquid includes a higher percentage of tin, so the point at which it freezes will be lower, and the remaining liquid will again contain a higher percentage of tin, so the point at which it freezes will be lower. This cycle will continue until the temperature drops below freezing. Because the two curves of the two borders will meet at this moment, all of the remaining mixture will freeze (this point called the eutectic point).
The melting temperature of the mixture will decrease more than the eutectic composition for joining the pipes in our situation (where the solder mixture contains 67 percent lead and 23 percent tin by weight). The mixture is more suitable for soldering if the melting temperature is lower. As a result, the tin and lead mixture is better for joining pipes.
Consider a completely miscible two-component system whose overall composition is x, at a temperature where liquid and gas phases coexist. The composition of the gas phase at this temperature is and the composition of the liquid phase is . Prove the lever rule, which says that the proportion of liquid to gas is . Interpret this rule graphically on a phase diagram.
Calculate the Helmholtz free energy of a van der Waals fluid, up to an undetermined function of temperature as in . Using reduced variables, carefully plot the Helmholtz free energy (in units of ) as a function of volume for Identify the two points on the graph corresponding to the liquid and gas at the vapor pressure. (If you haven't worked the preceding problem, just read the appropriate values off .) Then prove that the Helmholtz free energy of a combination of these two states (part liquid, part gas) can be represented by a straight line connecting these two points on the graph. Explain why the combination is more stable, at a given volume, than the homogeneous state represented by the original curve, and describe how you could have determined the two transition volumes directly from the graph of .
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