Second Law of Thermodynamics - UNSOLVED PRACTICE SET

Q7. State the Kelvin-Planck statement of the Second Law of Thermodynamics. What does it imply about the efficiency of heat engines?

Q8. State the Clausius statement of the Second Law of Thermodynamics. How is it related to the working of refrigerators?

Q9. What is a reversible process? Give two conditions necessary for a process to be reversible.

Q10. Explain why all natural processes are irreversible. Give two examples of irreversible processes from everyday life.

Q11. What is a perpetual motion machine of the second kind (PMM-2)? Why is it impossible to construct?

Q12. Explain the concept of entropy in one sentence. How does the Second Law relate to entropy?

Q13. State and explain both the Kelvin-Planck and Clausius statements of the Second Law of Thermodynamics. Show that these two statements are equivalent by proving that violating one leads to violation of the other. Use clear reasoning and diagrams.

Q14. Explain the concept of reversible and irreversible processes with examples. Discuss the factors that make a process irreversible in practice, such as friction, finite temperature differences, and non-quasi-static changes. Why is the concept of a reversible process important in thermodynamics despite being impossible to achieve perfectly?

Q15. A student proposes the following ideas. Analyze each using the Second Law of Thermodynamics and state whether it is possible or impossible:

(i) A heat engine that absorbs 1000 J from a reservoir at 400 K and converts all of it into work, rejecting no heat.

(ii) A refrigerator that extracts heat from a cold body and transfers it to a hot body without any external work.

(iii) A cyclic process in which the net entropy of the universe decreases.

(iv) A heat engine operating between 500 K and 300 K with an efficiency of 50%.

Q16. A heat engine operates between 600 K and 300 K. A designer claims the engine can achieve 55% efficiency.

(i) Calculate the Carnot efficiency for these temperatures.

(ii) Is the claimed efficiency possible? Justify using the Second Law.

(iii) If the engine absorbs 2000 J per cycle, what is the maximum possible work output?

(iv) What is the minimum heat that must be rejected per cycle?

(v) If the engine actually rejects 1000 J per cycle, what is its actual efficiency?

Q17. A refrigerator operates between –5°C (268 K) and 30°C (303 K). The manufacturer claims a COP of 10.

(i) Calculate the ideal (Carnot) COP for this refrigerator.

(ii) Is the claimed COP possible? Explain using the Second Law.

(iii) If the refrigerator extracts 500 J per cycle from the cold reservoir, what is the minimum work required?

(iv) What is the actual work required if the COP is 10?

(v) Calculate the heat rejected to the hot reservoir in both cases.

Q18. Consider a system where 2 kg of water at 80°C is mixed with 3 kg of water at 20°C in an insulated container. The specific heat capacity of water is 4186 J kg⁻¹ K⁻¹.

(i) Calculate the final equilibrium temperature of the mixture.

(ii) Calculate the entropy change of the hot water.

(iii) Calculate the entropy change of the cold water.

(iv) Calculate the total entropy change of the universe.

(v) Does this process violate the Second Law? Explain.