You had the best answer.

The only bit you forgot is that the recovered water is clean and free from anything that could negatively affect the boiler......and therefore far cheaper than making "new" clean boiler feed water....

The condenser does allow the reclamation of energy in that you only have to drop the temperature so that the steam changes state to water. Which then can be pumped back into boiler. Older power plants just vented the steam into the atmosphere. Took more energy to heat cold feed water.

Well, ya gotta have a closed heat cycle with area inside it. That area is a measure of the work you get. If you don't have two different temperatures, an ordinary heat cycle doesn't have any area. But, you gotta get a new professor if you got one that's never run a steam engine.

If you follow the cycle round it seems as though you can get rid of the condenser until you realise that the water in the boiler needs to be at a much higher temperature than the normal boiling temperature because it is at a much higher pressure.

The cycle efficiency of a steam turbine cycle, which is used in most electric power production in the world, is approximately 30-33%. The more vacuum developed by the condenser, the closer the cycle will be to ideal because the turbine efficiency is maximum with the maximum differential pressure.

The cycle efficiency can also be improved by preheating the condensate or Feedwater prior to the boiler using waste steam from the turbine. Power production turbines have many stages within each casing and often have multiple turbine casings and rotors coupled inline with the generator. The quality of the steam decreases as it passes through each stage of the turbine. The decrease in steam quality (increased moisture) would impact turbine efficiency and cause increased turbine casing erosion if not treated. That is why there are several ports built in between turbine stages to extract a small % of low quality steam. This helps improve the quality of steam going to the next turbine stage, and supplies steam for preheating the Feedwater using Feedwater heaters (steam to water heat exchanger). I work at a boiling water reactor plant. In our plant, the condensate in the condenser is approx. 100-120 deg F, depending on winter to summer, and is cooled by river water. The condensate is routed through 5 stages of Feedwater heaters that raise the temperature to approximately 350 deg F and is pressurized via Feedwater pumps to 1000 psig prior to the returning to the reactor (boiler). The reactor (boiler) boils the water at 1000 psig into high quality steam at 550 deg F. Newer plant designs with more stages of Feedwater Heaters and Moisture Separator Reheaters between the high pressure turbines and low pressure turbines have final Feedwater temperature (return to the boiler) at 420-450 deg F.

The combination of low back-pressure downstream of the turbine, moisture separation between turbine stages and as many stages of Feedwater heating as practical will give the best cycle efficiency for the turbine steam cycle.

The turbine for a power plant is designed based on many parameters including the range of backpressure (vacuum) that the turbine should be allowed to operate. The turbine controls monitor the backpressure and will trip the turbine off-line if the backpressure is too high (vacuum too low). If you tried to run a modern power plant designed with a condenser without the cooling for the condenser, the turbine and boiler would trip off. It is unlikely a turbine manufacturer or steam system supplier would design a plant without a condenser, because the efficiency of such a design would be so low that it would not be competition with current designs and would not be economical to operate.

Most plants have a thermal performance engineer that trends numerous parameters on a frequent basis including condenser vacuum, condensate and Feedwater temperature, and Feedwater flow rate. They also look for losses such as steam and water leaks, which are usually due to valve seat leakage, which routes back to the condenser. They worry about miniscule changes in cycle efficiency. The competition in the electric utility industry is very high, and management expects the plants to be at maximum efficiency as possible. The concept of having no condenser might sound good, but if it were more efficient to operate a steam turbine without a condenser, it would have been done already.

If I am reading the question correctly, the student is wondering why condese the steam at all and just send the exhaust vapour back to the boiler for re-heating. If this were possible, all the latent heat losses would be eliminated increasing cycle efficiency to upward of 80%. There is no practical method of compressing the vapour to above boiler pressure for return to the boiler (now would be considered a fired heater rather than a boiler).

Poor teaching.

What the second law states is that you cannot have an engine which accepts thermal energy and converts all of it to mechanical shaft power. Heat has to be absorbed at a high temperature and part of it has to be rejected at a lower temperature with the difference being converted (ideally) to shaft power. The steam engine is just a particular example where the boiler accepts heat at at high temperature and converts some of it to turbine shaft power while rejecting heat at low temperature in the condenser. If the phase change to liquid water were to be avoided as you suggest, then it would have to be heated as it is pressurised to the boiler pressure as it is re-introduced into the boiler, and then you will find that there would be no net mechanical power created ! So you cannot beat the second law.

I remember back in college when we were studying the 4 laws of thermodynamics, one of the students asked:

"Sir, who is Zeroth?"

and the reply was

"Well Zeroth must be one of the ancient scientists who formulated the laws of thermodynamics."

I guess your teacher asked the same question before.

The steam has to become water in order to be turned into steam again, it is the the pressure of the expansion of the water into steam that allows work to be done. An old fashioned locomotive just heated the water into steam and threw it away. A condensing engine is more efficient and some designs are even more efficient than internal combustion. By using the excess heat from the used steam and the boiler exhaust even higher efficiency is achieved, nearly 90%. Thermoelectric devices can make electricity directly from the excess heat and in a stationary unit, the excess heat can be used to heat buildings, water and air. By condensing only to just barely below the boiling point and using insulation to prevent heat loss from the steam a bit more efficiency can be gotten.

By building one of these small, highly efficient steam engines to produce electricity for an electric vehicle one could get many more miles of travel for the amount of fuel used. Build an EV that will go 70 mph for 25 miles which is not prohibitively expensive in battery costs, then add a steam engine powered generator that will recharge the batteries as needed. At home it can be plugged in to recharge.

Check out James Rumsey, the inventor of the steamboat, Stanley Steamers, Doble Steam cars, water tube boilers, the Lamont boiler, single and double-acting steam engines, compound steam engines, uniflow steam engines, Cyclone Steam Engines, Green Steam Engines, Lysholm expanders and the Tesla Turbine. You too may get enthused about steam as a cleaner and more efficient power source than internal combustion, which is also more easily able to use multiple fuels.