Critically evaluate the following situations. Some of the proposals or interpretations are reasonable, while others violate very basic principles of thermodynamics. a. it is commonly known that one can super cool water and maintain it as a liquid at temperatures as low as —10°C. If a sample of super cooled liquid water is isolated in a closed, thermally insulated container, after a time it spontaneously changes to a mixture of ice and water at 0°C. Thus, it increases its temperature spontaneously with no addition of heat from outside: furthermore, some low-entropy ice is produced.
b. An inventor proposed a new scheme for heating buildings in the winter in arctic climates. Since freezing temperatures reach only a few feet down into the soil, he proposes digging a well and immersing a coil of copper tubing in the water. He will then connect the ends of the coil to the radiators in the building and use a heat pump to transfer heat into the building. What would be your advice to an attorney who is assigned to evaluate this patent application? Base your evaluation on the relevant thermodynamics.
c. On a hot summer's day, your laboratory partner proposes opening the door of the lab refrigerator to cool off the room.
d. A sample of air is separated from a large evacuated chamber, and the entire system is isolated from the surroundings. A small pinhole between the two chambers is opened, and roughly half the gas is allowed to effuse into the second chamber before the pinhole is closed. Because nitrogen effuses faster than oxygen, the gas in the second chamber is richer in nitrogen, and the gas in the first chamber is richer in oxygen than the original air. The gases have thus spontaneously unmixed (at least partially), and this is held to be a violation of the Second Law of Thermodynamics.
e. Super cooled water at —10°C has a higher entropy than does an equal amount of ice at — 10°C. Therefore, super cooled water cannot go spontaneously to ice at the same temperature in an isolated system.
f. A volume of an aqueous solution of hydrogen peroxide is placed in a cylinder and covered with a tightfitting piston. A small amount of the enzyme catalase is placed on a probe and inserted through an opening in the base of the cylinder. The catalase catalyzes the decomposition of the hydrogen peroxide, and the oxygen formed serves to raise the piston. The catalase is then withdrawn and the hydrogen peroxide is reformed, causing the piston to return to its initial position. The piston is connected to an engine and net work is obtained indefinitely by cycles of simply inserting and withdrawing the catalase.