Thermodynamics — Advanced Notes & 50 MCQs

1. The first law of thermodynamics is basically a statement of:

1. Increase of entropy
2. Perpetual motion of the second kind
3. Conservation of energy ✅
4. Absolute zero temperature

2. For a reversible isothermal expansion of an ideal gas, the change in internal energy ΔU is:

1. Positive
2. Negative
3. Zero ✅
4. Depends on pressure

3. The sign convention w = -P_ext ΔV indicates:

1. Work done on the system is negative
2. Work done by the system is negative of system expansion ✅
3. Work is always positive
4. No work in expansion

4. Hess’s law is a consequence of which of the following?

1. Second law of thermodynamics
2. Ideal gas law
3. State function property of enthalpy ✅
4. Maxwell relations

5. ΔG° for a reaction at equilibrium is related to the equilibrium constant K by:

1. ΔG° = RT ln K
2. ΔG° = K/RT
3. ΔG° = -RT ln K ✅
4. ΔG° = -K/RT

6. Entropy has units of:

1. J
2. Pa
3. J·K⁻¹ ✅
4. kJ·mol⁻¹

7. For a spontaneous process at constant T and P, which quantity decreases?

1. Entropy of universe
2. Enthalpy of system
3. Gibbs free energy of system ✅
4. Internal energy always

8. The third law of thermodynamics states that:

1. ΔS is always positive
2. Entropy is independent of temperature
3. Entropy of a perfect crystal at absolute zero is zero ✅
4. Absolute zero cannot be reached

9. Entropy change for a reversible heat transfer at temperature T is:

1. ΔS = q/T only for irreversible
2. ΔS = q_rev / T ✅
3. ΔS = q × T
4. ΔS = 0 always

10. Which of the following is NOT a state function?

1. Enthalpy
2. Internal energy
3. Work ✅
4. Entropy

11. For an ideal gas, the internal energy depends only on:

1. Pressure
2. Temperature ✅
3. Volume
4. Number of moles only

12. The Helmholtz free energy A is defined as:

1. A = H + TS
2. A = U + PV
3. A = U - TS ✅
4. A = G + TS

13. At constant temperature and volume, spontaneity is determined by:

1. ΔG
2. ΔA (Helmholtz free energy) ✅
3. ΔH
4. ΔS only

14. Hess’s law allows calculation of reaction enthalpy by:

1. Measuring temperature change only
2. Using ideal gas law
3. Adding enthalpies of steps (state function) ✅
4. Calculating entropy changes

15. The standard free energy change ΔG° is 0 at:

1. All temperatures
2. At equilibrium only if ΔH° = 0
3. Equilibrium (when K = 1 gives ΔG° = 0) ✅
4. When ΔS° = 0 only

16. If ΔH < 0 and ΔS > 0 for a reaction, the reaction is:

1. Non-spontaneous at all temperatures
2. Spontaneous only at high T
3. Spontaneous only at low T
4. Spontaneous at all temperatures ✅

17. The Gibbs-Helmholtz equation relates ΔG and ΔH by:

1. ΔG = ΔH + TΔS
2. (∂(ΔG/T)/∂T)_P = -ΔH/T^2 (Gibbs-Helmholtz form) ✅
3. ΔG = ΔH - T^2 ΔS
4. ΔG = -RT ln K only

18. The entropy change for mixing two ideal gases is:

1. Zero
2. Positive ✅
3. Negative
4. Depends on pressure only

19. Which of the following processes is isentropic?

1. Irreversible adiabatic expansion
2. Reversible adiabatic process ✅
3. Isothermal reversible compression
4. Any process at constant pressure

20. Standard enthalpy of formation of an element in its standard state is:

1. Non-zero
2. Zero ✅
3. Undefined
4. Equal to entropy

21. The work done in a reversible isothermal expansion of ideal gas from V1 to V2 is:

1. w = -P_ext (V2 - V1)
2. w = -nRT ln(V2/V1) ✅
3. w = -nC_v ΔT
4. w = 0

22. Which potential is most useful for processes at constant T and P?

1. Internal energy U
2. Gibbs free energy G ✅
3. Helmholtz free energy A
4. Enthalpy H only

23. The maximum non-expansion work obtainable from a system at constant T and P is:

1. ΔH
2. ΔU
3. -ΔG ✅
4. ΔS

24. If ΔG° < 0 and ΔH° > 0, the reaction is spontaneous at:

1. Low temperatures only
2. High temperatures only ✅
3. All temperatures
4. No temperatures

25. A Carnot engine operating between T1 and T2 has efficiency:

1. 1 - T1/T2
2. 1 - T_cold/T_hot ✅
3. T_hot/T_cold
4. T_cold/T_hot

26. The Clausius statement of the second law says:

1. Heat cannot flow from cold to hot spontaneously
2. Heat cannot flow from cold to hot without external work ✅
3. Perpetual motion machine of the second kind is possible
4. Entropy of universe can decrease

27. The Kelvin-Planck statement refers to impossibility of:

1. Heat engine with 100% efficiency ✅
2. Engine operating between two reservoirs
3. Heat flow from cold to hot
4. Isothermal expansion

28. For a phase transition at equilibrium (e.g., liquid–vapor), ΔG is:

1. Positive
2. Negative
3. Zero ✅
4. Undefined

29. The relation ΔS = ΔH_rev / T is valid for:

1. Irreversible processes only
2. Reversible processes only ✅
3. All spontaneous processes
4. Isothermal irreversible processes

30. The standard molar entropy S° of substances at 298 K is always:

1. Zero for all substances
2. Positive for real substances (except perfect crystal at 0 K) ✅
3. Negative for liquids only
4. Equal to enthalpy

31. Which of the following is true about ΔG and spontaneity?

1. ΔG > 0 spontaneous
2. ΔG < 0 spontaneous ✅
3. ΔG = 0 non-spontaneous
4. ΔG independent of temperature

32. The Gibbs free energy change for a reaction depends on:

1. Only enthalpy change
2. Enthalpy, entropy, and temperature ✅
3. Only entropy change
4. Only temperature

33. For an ideal gas, the molar heat capacity at constant volume C_v,m is related to C_p,m by:

1. C_p,m = C_v,m
2. C_p,m = C_v,m - R
3. C_p,m = C_v,m + R ✅
4. C_p,m = 2 C_v,m

34. The Joule-Thomson coefficient is zero for ideal gases because:

1. They have intermolecular attractions
2. Their internal energy depends only on temperature ✅
3. They cannot expand
4. They have no entropy

35. The entropy change for mixing ideal gases is independent of:

1. Temperature
2. Pressure
3. Identity of gases (only depends on mole fractions) ✅
4. Number of moles

36. In an adiabatic reversible compression of an ideal gas, which quantity increases?

1. Entropy of system
2. Temperature of gas ✅
3. Entropy of universe
4. Gibbs energy decreases

37. The standard Gibbs free energy change ΔG° for a reaction at temperature T can be used to calculate K by:

1. K = e^(ΔG°/RT)
2. K = e^(-ΔG°/RT) ✅
3. K = ΔG°/RT
4. K = -RT/ΔG°

38. Which statement about reversible processes is true?

1. They occur quickly
2. They are idealized processes with no entropy production ✅
3. They always increase entropy
4. They happen only in engines

39. Which expression defines chemical potential μ for component i?

1. μ_i = U/ni
2. μ_i = (∂G/∂n_i)_{T,P,n_j} ✅
3. μ_i = H - TS
4. μ_i = ∂S/∂T

40. For phase equilibrium between liquid and vapor, the condition is:

1. ΔH > 0
2. μ_liquid = μ_vapor ✅
3. ΔS = 0
4. Only temperature equality

41. The Clapeyron equation relates which quantities?

1. Entropy and internal energy
2. Slope of phase boundary dP/dT = ΔH_trans / (T ΔV_trans) ✅
3. ΔG and ΔH only
4. Pressure and volume only

42. Which process decreases entropy of the system?

1. Melting of ice
2. Freezing of water ✅
3. Evaporation
4. Mixing of gases

43. The relation ΔH°(T2) = ΔH°(T1) + ∫_{T1}^{T2} ΔC_p dT is known as:

1. Hess's law
2. Kirchhoff’s law ✅
3. Clausius-Clapeyron
4. Gibbs-Helmholtz

44. An exergonic reaction is one that:

1. Absorbs free energy
2. Releases free energy (ΔG < 0) ✅
3. Has ΔH > 0 always
4. Is at equilibrium

45. Which quantity is maximized at equilibrium for a closed system at constant T and P?

1. Gibbs free energy
2. Entropy of the universe (or ΔG is minimized for the system) ✅
3. Internal energy
4. Enthalpy

46. In thermodynamics, a quasi-static process means:

1. Fast and irreversible
2. Infinitely slow, nearly reversible process ✅
3. Adiabatic by definition
4. Isothermal always

47. Which of the following is true for ideal solution?

1. ΔG_mix > 0
2. ΔG_mix = RT Σ x_i ln x_i (ideal entropy of mixing form) ✅
3. ΔH_mix is large and positive
4. Activity coefficients ≠ 1

48. The efficiency of any reversible heat engine depends only on:

1. Working substance
2. Heat source only
3. Temperatures of the hot and cold reservoirs ✅
4. Pressure difference only

49. For a chemical reaction with ΔH < 0 and ΔS < 0, the reaction will be spontaneous at:

1. All temperatures
2. Low temperatures ✅
3. High temperatures
4. Never spontaneous