EIT Thermodynamics 4 — Questions and Answers
Question 1: Which Maxwell relation is derived from the Gibbs free energy G = H - TS?
- (∂T/∂v)_s = -(∂P/∂s)_v
- (∂s/∂P)_T = -(∂v/∂T)_P (Correct answer)
- (∂T/∂P)_s = (∂v/∂s)_P
- (∂P/∂T)_v = (∂s/∂v)_T
Correct answer: (∂s/∂P)_T = -(∂v/∂T)_P
From dG = -sdT + vdP, the Maxwell relation (∂s/∂P)_T = -(∂v/∂T)_P follows from equality of mixed partials.
Question 2: An ideal Otto cycle operates with a compression ratio of 8 and k = 1.4. What is the thermal efficiency?
- 47.5%
- 56.5% (Correct answer)
- 36.5%
- 65.0%
Correct answer: 56.5%
η_Otto = 1 - 1/r^(k-1) = 1 - 1/8^0.4 = 1 - 1/2.297 ≈ 0.565 = 56.5%.
Question 3: For a psychrometric process, the dew point temperature is the temperature at which:
- Relative humidity reaches 50%
- Moisture begins to condense from air (Correct answer)
- Wet-bulb and dry-bulb temperatures are equal
- Air becomes fully saturated at constant pressure and enthalpy
Correct answer: Moisture begins to condense from air
The dew point is the temperature at which water vapor in moist air begins to condense when cooled at constant pressure.
Question 4: The Joule-Thomson coefficient μ_JT = (∂T/∂P)_h is zero for:
- Real gases at low temperature
- Steam above its critical point
- Ideal gases (Correct answer)
- Any gas at its inversion temperature
Correct answer: Ideal gases
For an ideal gas, enthalpy depends only on temperature, so throttling (constant-h) produces no temperature change, giving μ_JT = 0.
Question 5: In an air-standard Brayton cycle, increasing the pressure ratio (while maintaining the same temperature limits) will:
- Always decrease thermal efficiency
- Increase thermal efficiency up to a point determined by the temperature limits (Correct answer)
- Have no effect on efficiency
- Always increase net work output
Correct answer: Increase thermal efficiency up to a point determined by the temperature limits
Brayton cycle efficiency increases with pressure ratio, but the optimal pressure ratio for maximum work is determined by the temperature ratio.
Question 6: The third law of thermodynamics states that the entropy of a perfect crystalline substance at absolute zero temperature is:
- Equal to its enthalpy of formation
- Negative
- Zero (Correct answer)
- Indeterminate
Correct answer: Zero
The third law (Nernst theorem) establishes that the entropy of a perfect crystal at 0 K is exactly zero.
Question 7: Steam quality (x) of 0.75 in a two-phase mixture means:
- The temperature is 75% of the saturation temperature
- 75% of the mixture by mass is saturated vapor (Correct answer)
- The pressure is 75% of the critical pressure
- 75% of the mixture by volume is saturated liquid
Correct answer: 75% of the mixture by mass is saturated vapor
Quality x = m_vapor / m_total, so x = 0.75 means 75% of the mixture mass is saturated vapor.
EIT Thermodynamics 4
Which Maxwell relation is derived from the Gibbs free energy G = H - TS?