# Thermodynamics Questions and Answers – Clausius’ Theorem and the Inequality of Clausius

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This set of Thermodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Clausius’ Theorem and the Inequality of Clausius”.

1. Any reversible path can be substituted by a reversible zigzag path between the same states.
a) true
b) false

Explanation: It should consist of a reversible adiabatic, followed by a reversible isotherm and then by a reversible adiabatic.

2. According to the Clausius’ theorem, the cyclic integral of ____ for a reversible cycle is zero.
a) dW/dT
b) dH/dT
c) dQ/dT
d) dE/dT

Explanation: Q is the total heat supplied or heat rejected in the complete cycle.

3. Two reversible adiabatic paths can intersect each other.
a) true
b) false

Explanation: If we assume they intersect, then the Kelvin-Planck statement of the second law will be violated.

4. The efficiency of a general cycle will be _____ the efficiency of a reversible cycle.
a) equal to
b) less than
c) equal to or greater than
d) equal to or less than

Explanation: The efficiency of a reversible cycle is maximum.

5. The cyclic integral of entropy is____
a) one
b) zero
c) infinity
d) cannot be determined

Explanation: The cyclic integral of any property is zero and entropy is a property.

6. Which of the following is known as the inequality of Clausius?
a) cyclic integral of dQ/T<=0
b) cyclic integral of dQ/T>=0
c) cyclic integral of dW/T<=0
d) cyclic integral of dW/T>=0

Explanation: It provides the criterion for the reversibility of a cycle.

7. If the cyclic integral of dQ/T is zero then the cycle is
a) irreversible but not possible
b) irreversible but possible
c) impossible
d) reversible

Explanation: This comes from the inequality of Clausius.

8. If the cyclic integral of dQ/T is less than zero then the cycle is
a) irreversible but not possible
b) irreversible and possible
c) impossible
d) reversible

Explanation: This comes from the inequality of Clausius.

9. If the cyclic integral of dQ/T is greater than zero then the cycle is
a) irreversible but not possible
b) irreversible but possible
c) impossible
d) reversible

Explanation: This comes from the inequality of Clausius.

10. If dQ is the heat supplied at T and dQ2 is the heat rejected at T2, then efficiency is given by
a) 1-(dQ2/dQ)
b) 1-(dQ/dQ2)
c) (dQ/dQ2)-1
d) (dQ2/dQ)-1

Explanation: Efficiency is given by = 1-(heat reached/heat supplied).

11. A heat engine receives 6 kW from a source at 250°C and rejects heat at 30°C with W. = 0 kW. Does this satisfy the inequality of Clausius?
a) yes
b) no
c) cannot be said
d) none of the mentioned

Explanation: ⌠ dQ/T = (6000/523) – (6000/303) = –8.33 kW/K < 0. [/expand] 12. A heat engine receives 6 kW from a source at 250°C and rejects heat at 30°C with W. = 6 kW. Does this satisfy the inequality of Clausius? a) yes b) no c) cannot be said d) none of the mentioned [expand title="View Answer"]Answer: b Explanation: ⌠ dQ/T = (6000/523) - (0/303) = 11.47 kW/K > 0.

Sanfoundry Global Education & Learning Series – Thermodynamics.
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