Practice Questions on Second Law of Thermodynamics with Answers.

**Questions on Second Law of Thermodynamics with Answers**

*Q1. A thermally ‘insulated box of volume 2V has a partition which divides it into two chambers of equal volume. Each chamber contains He gas at temperature T and pressure P. On removing the partition, the molecules in the two chambers mix with each other. The change in entropy of the system is*

*(a) –*^{PV}/_{T}ln2*(b) 0**(c)*^{PV}/_{T}ln2*(d)*^{2PV}/_{T}ln2

*Q2. Which of the following statements is correct?*

*(a) a) You can construct an engine operating in cycles, extracting heat Q and performing exactly equivalent work W.**(b) You can construct an engine operating in cycles extracting heat Q and performing more than equivalent amount of work W.**(c) You can have an engine operating cyclically such that the entropy remains constant throughout the cycle.**(d) You cannot construct a cyclically operating engine that will extract heat Q and perform exactly equivalent amount of work W.*

*Q3. The sole effect of a hypothetical thermodynamic process E _{1} is to convert an amount Q of heat entirely into work. A second hypothetical process E_{2} converts an amount W of work entirely into heat. It can be said that the second law of thermodynamics is violated by*

*(a) E*_{1}but not E_{2}*(b) E*_{2}but not E_{1}*(c) Both E*_{1}and E_{2}*(d) neither processes*

**Q4. Which of the following is true?**

*(a) In an engine the magnitude of entropy change is larger of the source than at the sink**(b) When two gases at identical temperature and pressure are mixed, the entropy remains unchanged**(c) The only case where entropy of the universe stays constant is in the ideal Carnot’s engine**(d) The efficiency of a refrigerator is more in winters than in summers, assuming that the inside temperature attained in the refrigerator is the same in both cases.*

*Q5. The internal energy of a system is expressed by function U(S,V) = S ^{4/3} V^{α }, where α is a constant. The value of α is*

*(a) 1**(b)*^{1}/_{3}*(c) –*^{1}/_{3}*(d)*^{3}/_{4}

*Q6. The value of entropy at absolute zero of temperature would be*

*(a) Zero for all the materials**(b) Finite for all the materials material**(c) Zero-for some materials and non-zero for others**(d) Unpredictable for any material*

*Q7. Nernst heat theorem is another way of stating*

*(a) first law of thermodynamics**(c) third law of thermodynamics**(b) second law of thermodynamics**(d) fourth law of thermodynamics*

**Q8. Which of the following best describes the relation between isothermal compressibility (κ _{T}) and adiabatic compressibility (κ_{s}) is**

*(a) κ*_{T}> κ_{s}*(b) κ*_{T}≥ κ_{s}*(c) κ*_{T}< κ_{s}*(d) κ*_{T}≤ κ_{s}

*Q9. A thermally insulated cubical box has two chambers of equal volume. Initially one mole of a mono atomic ideal gas is placed in one of the chambers while the other chamber is kept empty. The gas slowly leaks through a small hole and eventually occupies the whole box. The change in entropy of the gas is given by*

*(a)*^{R}/_{ln2}*(b) R ln2**(c) zero**(d) 2R*

**Q10. The change in entropy (in SI units) in an adiabatic free expansion of one mole of an ideal gas, to double its initial volume is**

*(a) 5.762**(b) 0**(c) 8.314**(d) 1.38*

*Q11. Consider a gas contained in a box at pressure P and temperature T having entropy S. If the box is divided into two parts of volume V _{1} and V_{2} with corresponding entropies S_{1} and S_{2} , then S-(S_{1}+S_{2}) is*

*(a) > 0**(b)*< 0*(c)*= 0*(d)*none of these

*Q12. The Clausius mathematical statement of the second law of thermodynamics, for an irreversible process is*

*(a) ∮*^{δQ}/_{T}≤ 0*(b) ∮*^{δQ}/_{T}> 0*(c) ∮*^{δQ}/_{T}< 0*(d) ∮*^{δQ}/_{T}= 0

*Q13. For any process, the second law ofthermodynamics requires that the change ofentropy ofthe universe be*

*(a) positive only**(b) positive or zero zero only**(c) zero only**(d) negative or zero*

**Q14. A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole on an ideal gas A and the other compartment contains one mole of a different ideal gas B . The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that tie gases are chemically inert. The change in the total entropy of the gases on mixing is**

*(a) 0**(b) R ln2**(c)*^{3}/_{2}R ln2*(d) 2R ln2*

**Q15. Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium,**

*(a) the total entropy of the final system is the same as the sum of the entropy of the individual system always.**(b) the entropy of mixing is 2Nk*_{B}ln2.*(c) the entropy of the final system is less than that of sum of the initial entropies of the two gases**(d) The entropy of mixing is non-zero when the atoms A and B are of the same type.*

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*Answer Key* (if you find any answer wrong, feel free to Correct us)

*Answer Key*

01. | (b) | 06. | (c) | 11. | (b) |

02. | (d) | 07. | (c) | 12. | (c) |

03. | (a) | 08. | (a) | 13. | (b) |

04. | (b) | 09. | (b) | 14. | (d) |

05. | (c) | 10. | (a) | 15. | (b) |