Thermodynamic Cycles Quiz: Otto, Diesel, Rankine, Refrigeration

Concept: Otto = spark-ignition engine model. Otto cycle models spark-ignition internal combustion engines. It is an idealised description of how many petrol engines convert heat from combustion into work.

Concept: Diesel = compression-ignition model. Diesel cycle models compression-ignition engines. Fuel ignites due to high temperature from compression rather than a spark.

Concept: Rankine = steam power cycle. Rankine cycle is the standard steam power cycle. It uses a boiler, turbine, condenser, and pump to convert heat into electrical power.

Concept: Both are engine cycles. They convert some heat released from combustion into work. In both cases, not all heat becomes work, so waste heat must be rejected.

Concept: Condenser rejects heat and closes the cycle. Condenser rejects heat and helps close the cycle. It turns steam back into liquid so the pump can pressurise it efficiently for the boiler.

In a steam plant, the boiler serves as the component where heat is transferred to the working fluid, typically water, to convert it into steam. This process involves burning fuel or using another heat source to raise the temperature of the water, thereby increasing its energy content. The addition of heat causes the water to boil and produce steam, which is essential for driving turbines and generating electricity. Thus, the term "added" accurately describes the function of the boiler in facilitating this crucial energy transformation.

Concept: Pump pressurises liquid efficiently. Pump pressurizes liquid water for the boiler. Pressurising liquid requires relatively little work compared with compressing a gas.

Concept: Liquids are nearly incompressible. Liquids are far less compressible than gases, so pressure increase needs less volume change. That’s why Rankine cycles use a pump on liquid water rather than compressing steam.

Concept: Refrigeration is the reverse direction. Refrigeration is a reversed cycle requiring work input. It uses work to pump heat from a colder region to a warmer region.

Concept: Counterclockwise = net work done on the system. Counterclockwise indicates net work is done on the system. This matches the need for energy input in refrigeration.

Concept: Phase change cycles move lots of energy. Rankine uses water/steam; refrigeration uses refrigerant evaporating/condensing. Otto and diesel cycles are usually treated as gas-phase cycles in their idealised models.

Concept: Otto idealisation. Otto model: heat addition at constant volume (idealised). This represents rapid combustion occurring faster than significant volume change.

Concept: Diesel idealisation. Diesel model: heat addition at constant pressure (idealised). This represents fuel burning while the piston continues moving, keeping pressure roughly constant during that phase.

Concept: Real processes are irreversible. Friction, turbulence, heat leaks, and finite gradients create irreversibility. These losses increase entropy and reduce the fraction of energy that becomes useful work.

Concept: Larger temperature difference raises the upper limit. Larger temperature difference allows higher theoretical efficiency. It increases the maximum possible work that can be extracted for a given heat input.

In a complete thermodynamic cycle, the change in internal energy (Δu) is zero, indicating that the system returns to its initial state. According to the first law of thermodynamics, the net heat added to the system (q_net) is equal to the work done by the system (w_net) during the cycle. Since there is no net change in internal energy, all energy transferred as heat is converted into work, leading to the conclusion that q_net equals w_net.

Concept: Work = heat in - heat out. W = q_h - q_c = 10,000 - 7,500 = 2,500 J. The difference between absorbed and rejected heat is the net work output.

Concept: Efficiency calculation. η = W/q_h = 2500/10,000 = 0.25. That means 25% of the input heat becomes useful work.

Concept: First law counts energy; second law sets direction/limits. Second law sets limits and explains why refrigerators need work input. Both devices conserve energy, but only some energy conversions are allowed spontaneously.

Concept: Models vs reality. Real cycles are approximations of ideal models, limited by the second law. Irreversibility (entropy production) explains why real devices fall short of ideal performance.