Test: Second Law of Thermodynamics - 1 - Mechanical Engineering MCQ

The Kelvin-Planck statement of the second law of thermodynamics asserts that:
"It is impossible for any device to operate in a thermodynamic cycle and produce work while exchanging heat only with a single reservoir."

Key Points:

• Option C directly captures this principle: an engine must discharge some heat to a second reservoir (lower temperature) to produce work in a cyclic process.

• This emphasizes the irreversibility of heat engines and the necessity of waste heat.

Why Other Options Are Incorrect:

• A: Relates to energy conservation (first law), not the second law.

• B: Reflects the Clausius statement (heat cannot spontaneously flow from cold to hot without work).

• D: Describes a first-law relationship (work = heat input - heat output), not the Kelvin-Planck limitation.

Conclusion:
The correct answer is C, as it encapsulates the Kelvin-Planck focus on the impossibility of a 100% efficient heat engine.

According to the Clausius statement of the second law:

• Heat flows from a cold surface to a hot surface without any assistance.
• Heat flows from a hot surface to a cold surface without any assistance.
• Heat can flow from a cold surface to a hot surface with the help of external work.

Among these statements:

• Statement 1 is incorrect; heat naturally flows from hot to cold.
• Statement 2 is correct; heat does flow from hot to cold surfaces.
• Statement 3 is also correct; external work can enable heat to flow from cold to hot.

Thus, the correct statements are 2 and 3.

Such a heat engine is PMM2 which is impossible. It violates kelvin-Plank statement

It may not be a reversible heat pump. So we use only heat data to get COP

Hence, the correct option is (c).

(decreasing lower temperature by ΔT)

(increasing higher temperature by ΔT)

So, the more effective way to increase the cycle efficiency is to decrease lower temperature.

Actual efficiency is more than the 2nd law efficiency which is impossible.

When a system takes an infinitely long time to execute a process through a finite gradient, the nature of that process changes significantly.

This scenario can be understood in the following ways:

• Reversibility: The process becomes reversible, meaning it can return to its original state without any net change to the system or surroundings.
• Irreversibility: If the process were to remain irreversible, it would not allow for a return to the original state without external intervention.
• Isothermal Conditions: In an isothermal process, the temperature remains constant. Given infinite time, the system can equilibrate, maintaining a steady temperature.
• Adiabatic Process: This type of process occurs without heat transfer. However, it can also involve changes in temperature depending on the conditions.

In summary, when the execution time is infinitely large through a finite gradient, the process tends towards becoming isothermal, where temperature stabilises due to prolonged interaction.

The statement "Heat cannot be transported from a system at low temperature to another system at high temperature without the aid of external agency" is the Clausius statement of the second law of thermodynamics. It emphasizes that heat naturally flows from hot to cold, and reversing this process (e.g., refrigeration) requires external work.

Key Points:

• Rudolf Clausius formulated this version of the second law, focusing on the directionality of heat transfer.

• Other options are unrelated:

  • B (Joule-Thomson): Associated with the throttling process in gases.

  • C (Max Planck): Known for quantum theory, not thermodynamics.

  • D (Gay-Lussac): Linked to gas laws (pressure-temperature relationships).

Conclusion: The correct attribution is Clausius, as his statement directly addresses the necessity of external work for heat transfer from cold to hot.

Heat removal rate, Q₂ = 7.2 kW

Power input to the compressor W = 1.8 kW

The coefficient of performance (COP) of the refrigerator can be calculated using the relation 

Hence the correct answer is 4.0

For reversible engine,

For reversible refrigerator

.

Hence, product for reversible thermodynamic cycle is not equal to 1.

For CE₁:

For CE2:

Hence, the correct answer is 50.