Clausius Statement Questions

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Very Short Answers Questions [1 Mark Question]

Ques. The efficiency of a heat engine cannot be 1, which among the following laws of thermodynamics agrees with this statement?

1. First
2. Second
3. Third
4. Zeroth

Ans. The correct answer is b. Second

Explanation: The second law of thermodynamics states that in an irreversible process, the entropy change has to be positive. Hence all the heat given to an engine cannot be converted into work. Therefore the efficiency of a heat engine cannot be 1.

Ques. Which among the following statements is the Kelvin Planck statement?

1. For a reversible cyclic process, efficiency can be 1
2. Without external work, heat from a cold reservoir can’t be transferred to a hot reservoir
3. The heat engine has an efficiency of fewer than 1
4. If the process is reversible, then the heat from a hot reservoir can be fully converted into work.

Ans. The correct answer is c. The heat engine has an efficiency of fewer than 1

Explanation: According to Kelvin Planck's statement no process is possible whose result is the absorption of heat from a reservoir and the complete conversion of heat into work. Therefore the efficiency of a heat engine is less than 1.

Ques. Which among the following is the statement of the second law of thermodynamics?

1. The second law talks about the probability to build a perfect engine
2. Energy is conserved in the second law of thermodynamics
3. The entropy of a system can never decline
4. Over time, the entropy of an isolated system can never decrease.

Ans. The correct answer is d. Over time, the entropy of an isolated system can never decrease.

Explanation: According to the second law of thermodynamics the entropy of an isolated system over time can never decrease. If there is a decrease in entropy of a system then at the same time, the entropy of another system will increase to compensate for that decrease in that process.

Ques. It is possible for the entropy of one system to decrease if a process is carried out between 2 systems.

1. True
2. False

Ans. The correct answer is a. True

Explanation: Yes, if the net entropy change of a system is positive then it is possible for the entropy of one system to decrease ensuring the entropy of the second system should increase adequately.

Ques. According to the first law of thermodynamics, a book lying on a table can fly upwards on its own by using the internal energy of the table.

1. True
2. False

Ans. The correct answer is a. True

Explanation: Energy is conserved in the above-mentioned case and according to the first law, this is valid. It only violates the second law.

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Short Answers Questions [2 Marks Questions]

Ques. What is Clausius's Statement?

Ans. According to the second law of thermodynamics, Clausius's statement states

“No process is possible whose sole result is the transfer of heat from a cooler object to a hotter object.”

Ques. State and explain the Second Law of thermodynamics.

Ans. The Second Law of Thermodynamics states that the state of entropy of an isolated system will always increase over time. It also states that the changes in the entropy in the universe can never be negative. In other words, it states that heat energy can never transfer from a body at a lower temperature to a body at a higher temperature without the addition of external energy.

Ques. What are the four different laws of thermodynamics?

Ans. The four different laws of thermodynamics are

• Zeroth Law of Thermodynamics
• First Law of Thermodynamics
• Second Law of Thermodynamics
• Third Law of Thermodynamics

Ques. State Carnot Theorem.

Ans. According to Carnot's Theorem, “No heat engines have efficiency more than that of the Carnot engine”.

• The efficiency of the Carnot engine depends on the temperature of the source and the sink.
• The efficiency of the Carnot engine is independent of the nature of the working substance.

Also Read:

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Long Answers Questions [3 Marks Questions]

Ques. A Carnot engine has an efficiency of 60%. If the source is at 527 ℃, then find the temperature of the sink.

Ans. Given

• The temperature of the source, T₁ = 527 ℃ = 527 + 273 = 800 K
• The efficiency of the Carnot engine, μ = 60% = 60/100

The formula for the efficiency of the Carnot engine is given by

μ = 1 - (T₂/T₁)

⇒ 60/100 = 1 - (T₂ / 800)

⇒ T₂ = 320 K

⇒ T₂ = 320 - 273 = 47 ℃

Ques. Find the efficiency of the Carnot engine whose source and sink are at 327 ℃ and 27 ℃.

Ans. Given

• The temperature of the source, T₁ = 327 ℃ = 327 + 273 = 600 K
• The temperature of the sink, T₂ = 27 ℃ = 27 + 273 = 300 K

The formula for the efficiency of the Carnot engine is given by

μ = 1 - (T₂/T₁)

⇒ μ = 1 - (300 / 600)

⇒ μ = 0.5

In percentage, μ = 0.5 x 100 = 50%

Ques. The coefficient of performance of a Carnot refrigerator is 9. If the heat is extracted from its sink is 900 J, then what amount of heat transferred to the source?

Ans. Let Q₁ be the amount of heat transferred to the source

Given

• The coefficient of performance of a Carnot refrigerator, ∏ = 9
• The heat extracted from the sink, Q₂ = 900 J

Coefficient of performance, ∏ = Q₂/W

Where W is the work done by the external agent.

Also, we have Q₁ = W + Q₂

⇒ W = Q₁ - Q₂

Therefore, the coefficient of performance, ∏ = Q₂/(Q₁ - Q₂)

⇒ 9 = 900/(Q₁ - 900)

⇒ Q₁ = 1000 J

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Very Long Answers Questions [5 Marks Questions]

Ques. Write some applications of the Second Law of thermodynamics.

Ans. The applications of the Second Law of thermodynamics are

• All heat engines, such as internal combustion and steam engines work on the second law of thermodynamics. 
• The coefficient of performance in refrigerators and heat pumps is determined by the second law of thermodynamics.
• Entropy can be calculated using the second law of thermodynamics is used to optimize the systems like power plants, heat exchangers, and chemical reactions.
• The efficiency limit of any heat engine is determined by the Carnot cycle, which is based on the second law of thermodynamics.
• The second law of thermodynamics states that not all energy is converted into useful work without some loss in energy.

Ques. Explain how Clausius' statement of the Second Law relates to the concept of entropy.

Ans. The measure of the degree of disorder and randomness in a system is known as Entropy. 

• It is the unavailability of the thermal energy of the system for conversion into work.
• The entropy of the colder body increases when heat is transferred from a hotter body to a colder body.
• While the entropy of the hotter body decreases.

According to Clausius's statement, the transfer of heat from a colder body to a hotter body is not possible without external work. 

• As per the second law of thermodynamics, this external input work is necessary to maintain heat flow direction.
• If the heat is transferred from a colder body to a hotter body then it violates the principle of entropy.

Ques. What is a reversible process? Mention the requirements for a process to be reversible.

Ans. The reversible process is those in which at any stage of the process it can be transversed back in the opposite direction in such a way that the system passes through exactly the same conditions at every step in the reverse process as in the direct process.

The basic requirements for a process to be reversible are

• The process should take place very slowly i.e. under quasi-static conditions.
• The pressure difference between working substances and surrounding at any stage of the process should be very small.
• There should be no friction.
• There should be no loss of energy.

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