Consider the following âperpetual motionâ device built around a concentration cell:
(a) Two copper electrodes are placed in copper sulfate solutions of equal concentration and connected to form a concentration cell. Initially there is no voltage in the cell. Assume that each electrode contains more copper than is present in either solution.
(b) Solution A is diluted until its Cu2+ concentration is cut in half, at which point the cell has a potential, E. The cell is run and useful work is done on the surroundings until the concentrations in the two solutions are equalized, at which time the cell voltage has fallen to zero again.
(c) Solution B is diluted until its Cu2+ concentration is halved, at which time the cell has the same potential, E as before, but in the opposite direction. Again the cell is run, and work is done until the concentrations in solutions A and B are the same.
(d) Steps (b) and (c) are repeated, diluting first one solution and then the other by halving its Cu2+ concentration after equilibrium has been attained in the previous step. Since neither concentration ever falls to zero by the halving process, we can maintain this process as long as we like and take an infinite amount of work out of the cell. The operation of the cell actually helps us, for it raises the concentration of the solution that we had just diluted.
What is wrong with this analysis?
Consider the following âperpetual motionâ device built around a concentration cell:
(a) Two copper electrodes are placed in copper sulfate solutions of equal concentration and connected to form a concentration cell. Initially there is no voltage in the cell. Assume that each electrode contains more copper than is present in either solution.
(b) Solution A is diluted until its Cu2+ concentration is cut in half, at which point the cell has a potential, E. The cell is run and useful work is done on the surroundings until the concentrations in the two solutions are equalized, at which time the cell voltage has fallen to zero again.
(c) Solution B is diluted until its Cu2+ concentration is halved, at which time the cell has the same potential, E as before, but in the opposite direction. Again the cell is run, and work is done until the concentrations in solutions A and B are the same.
(d) Steps (b) and (c) are repeated, diluting first one solution and then the other by halving its Cu2+ concentration after equilibrium has been attained in the previous step. Since neither concentration ever falls to zero by the halving process, we can maintain this process as long as we like and take an infinite amount of work out of the cell. The operation of the cell actually helps us, for it raises the concentration of the solution that we had just diluted.
What is wrong with this analysis?
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