ME301
Applications of Thermodynamics

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Catalog Description: (Prerequisities: ES 201 with a grade of C or better or CE205) Extends the conservation and accounting framework to examine energy-conversion systems. Topics include thermodynamic properties of pure substances, gas mixtures, exergy analyses, power and refrigeration cycles, psychrometric processes, combustion, and propulsion.




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Concept questions

Concept questions

Week 0: 

  • Write the good ole ConApps conservation of energy equation for
    • a steady-state system
    • a closed system over a finite time
    • all of the above with no KE or PE
    • all of the above with Wout assumed to be positive. (I.e., the opposite of the sign convention you learned.)
  • Write the good ole ConApps accounting of entropy equation for
    • a steady-state system
    • a closed system over a finite time
    • all of the above for an internally reversible process/system
    • all of the above for an adiabatic process/system
    • all of the above for an adiabatic and internally reversible process/system
  • How many intensive, independent properties do you need to fix the state of a simple, compressible substance?
  • Indicate whether the state of water fixed for each of the following conditions.
    • P and T are known and the water is evaporating.
    • P and T are known and the water is a compressed liquid.
    • P and v are known and the water is evaporating. T and h are known and the water is a superheated vapor. P is known and the water is a saturated vapor.
  • True/false: The entropy of air (S) is a function of T only.
  • True/false: The enthalpy of air (H) is a function of T only.
  • True/false: The specific enthalpy of air (h) is a function of T only.
  • True/false: The specific entropy of air (s) is a function of T only.
  • True/false: The specific entropy of incompressible liquid water (s) is a function of T only.
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Week 1

  • Explain the difference between an extensive property and an intensive property. Give an example of each.
  • Write the ideal gas equation five different ways. (Don't write one equation standing up, sitting down, standing on your head, in the bath tub and using your foot. I want five different equations.)
  • Prove that kPa*m3 = kJ. (Man that's easy! Why do we care? It shows up a lot in pdV work, and also in the ideal gas equation.)
  • Prove that for an ideal gas, R = cp - cv. Hint: Find expressions for du and dh for an ideal gas, and then use the definition of h to relate them to each other.)
  • Explain the difference in the following equations:
    • s2 - s1 = so(T2) - so(T1) - R*ln(P2/P1)
    • s2 - s1 = cp*ln(T2/T1) - R*ln(P2/P1)
  • A piston-cylinder assembly containing an ideal gas initially at 20°C undergoes a reversible, adiabatic expansion. The piston is weighted such that the process is also isobaric (i.e., constant pressure.) What is the final temperature? Why?
  • Why is the expansion in the last question not an expansion at all?
  • Consider a rigid, insulated container which is evacuated except for an air-filled balloon. A Maxwellian Demon pops the balloon such that the air expands and fills the entire tank.


  • demon.gif

    • For the entire container, what is the work? the heat transfer? the change in internal energy?
    • If air is an ideal gas, what is its change in temperature?
    • If air is an ideal gas, is its change in entropy less than, greater than or equal to zero? Is the entropy generation less than, greater than or equal to zero? Does this make sense from a reversibiity standpoint?

    Week 2

    • Why is the relationship between pressure, specific volume (or density) and temperature so important?
    • The State Postulate for a simple compressible substance says I need two independent intensive properties to fix its state. (I.e., find all the other properties.) Can I fix the state if I know
      • it's a vapor and I have values for V (big V) and T?
      • it's a liquid and I have values for ρ and P?
      • it's a saturated liquid/vapor mix and I have values for T and P?
      • it's a vapor and I have values for T and s (little s)?
    • Get some Play-Doh© and make a p-v-T surface. Use different colors for the phase regions.
    • What is the first determination you should always make in finding a property of a real substance? Which set of tables do you always consult first?
    • Why does it take longer to hard boil an egg in Denver than in Terre Haute?
    • Describe a process whereby you can take liquid water and eventually change it into water vapor without evaporating it.
    • Why are the compressed liquid tables so brief, or in some cases, non-exisitent?
    • A saturated vapor (Buzza buzzaa buzz!) is heated at constant volume. What is the phase after the heating takes place? Why?
    • Starting with the most general form (rate form) of the Conservation of Energy, apply it to a closed system undergoing a finite change in state to get U2 - U1 = Q1→2 + W1→2. What additional assumptions did you make?
    • Calculate h2 - h1 (specific enthalpy change) for superheated water as it goes from 1 MPa, 300°C to 1 MPa, 301°C (a 1°C change). Now calculate the required ΔV (change in velocity) to make V22/2 - V12/2 equal to the same value. (Pay attention to your units here!) See why we usually neglect KE effects?
    • What set of tables has properties for temperatures and pressures above the critical point?



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    Week 3

    • Using the Entropy Accounting Principle for a closed system undergoing a finite change in state, prove the statement: Any two of the three terms adiabatic, reversible and isentropic imply the third.
    • Using the Entropy Accounting Principle for a steady-state open system with one inlet and one exit, prove the statement: Any two of the three terms adiabatic, reversible and isentropic imply the third.
    • A saturated vapor is expanded at constant temperature until the volume doubles. How does the entropy change? (Up, down or the same) Why? Hint: sketch a T-v diagram first and then a T-s diagrams for the process.
    • A saturated vapor is expanded at constant pressure until the volume doubles. How does the entropy change? Why? (See hint above.)
    • Why are isentropic efficiencies sometimes called adiabatic efficiencies?
    • Is there a such thing as an isentropic efficiency for a boiler? Why or why not?
    • True/false: If the isentropic efficiency of a device is 1, then it necessarily operates reversibly.
    • True/false: If a device operates reversibly, then it necessarily has an isentropic efficiency of 1.
    • A turbine operating at steady-state is not a cyclic device. A compressor operating at steady-state is not a cyclic device. Niether is a boiler or a pump. How is it, then, that all things things operating together can form a cycle?
    • If you run the fluid in a closed-loop steady-state power plant cycle backwards, you get a refrigeration cycle. Why is there almost always a throttling valve instead of a turbine in this reversed cycle?
    • Explain why resistance heating is really not so wonderful. Hint: look at the COP for a heat pump and use the conservation of energy to put limits on its value.
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    Week 4: 

    • What is exergy?
    • What is meant by the dead state?
    • Name two ways that exergy can be transported into or out of a closed system.
    • Name three ways that exergy can be transported into or out of an open system.
    • Where does exergy transport occur, at a system boundary or inside the system?
    • Where does exergy destruction occur, at a system boundary or inside the system?
    • Explain the difference between work and useful work.
    • Heat transfer in the amount of 100 kJ is added to a system from a reservoir at 1200 K. If the environment is at 300 K and 100 kPa, how much exergy has been added to the system?
    • Work in the amount of 100 kJ is added to a constant volume system. If the environment is at 300 K and 100 kPa, how much exergy has been added to the system?
    • Work in the amount of 100 kJ is added to a system. The system's volume increases from 1 m3 to 2 m3 during the work addition. If the environment is at 300 K and 100 kPa, how much exergy has been added to the system?
    • Explain the difference between an efficient based on energy and an exergetic efficiency.
    • Explain the difference between an exergetic efficiency and an efficiency based on energy.
    • Explain the difference between specific exergy (a) and specific flow exergy (af). Why do we need flow exergy?
    • An open system operating at steady-state delivers 120 kW of power. If the surroundings are at 300 K and 100 kPa, what is the useful power ouput?
    • An open system operating at steady-state delivers 120 kW of power. If the surroundings are at 300 K and 100 kPa, what is rate of exergy ouput due to power?
    • At a certain instant in time an open system delivers 120 kW of power as its volume is changing at a rate of dV/dt = 1 m3/s. If the surroundings are at 300 K and 100 kPa, what is the useful power ouput?
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    Week 5:

    • Name the four pieces of equipment in a basic Rankine cycle and describe their functions.
    • Sketch an ideal Rankine cycle on a T-s diagram.
    • How do the expressions for isentropic efficiency (AKA, adiabatic) efficiency) for a pump and a turbine compare? Why?
    • What temperature must you use when calculating the rate of entropy transport into a system due to heat transfer?
    • Explain why cycle efficiency for a Rankine cycle goes up when the boiler pressure is increased.
    • Explain why cycle efficiency for a Rankine cycle goes up when a reheater is introduced between two turbine stages.
    • Explain why cycle efficiency for a Rankine cycle goes up when a regenerator (feedwater heater) is introduced before the boiler.
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    Week 6:

    • What is the difference between a gas power cycle and a vapor power cycle?
    • Sketch the T-s and P-v diagrams for
      • an ideal Otto cycle
      • an indeal Diesel cycle
      • and ideal Brayton cycle
    • How does the efficiency of an Otto cycle vary with compression ratio?
    • How does the efficiency of a Diesel cycle vary with compression ratio?
    • What is a cut-oof ratio? Does an Otto cycle have one? Does an Diesel cycle have one?
    • True/false: Compression ratio is r = vmax/vmin.
    • True/false: Compression ratio is r = Pmax/Pmin.
    • Can an ideal gas be throttled to a low temperature? Why or why not?
    • Sketch the T-s diagram for an ideal vapor-compression refrigeration cycle.
    • What is the difference between a refrigerator and a heat pump?
    • What is the measure of performance for a refrigerator? for a heat pump?
    • Explain why a two-stage compression refrigeration cycle including an intercooler usually results in higher cycle coefficient of performance.
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    Week 7:

    • mi = niMi and mdot,i = ndot,iMi. Does mfi = yiMi?
    • True/false: A volumetric analyis of an ideal gas mixture is the same as a mole analysis.
    • True/false: A volumetric analyis of an ideal gas mixture is the same as a mass analysis.
    • A mixture consists of 20% N2 and 80% CO2 by volume. The pressure, temperature and volume of the mixture are 100 kPa, 300 K and 1 m3, respectively.
      • True/false: The temperature of the N2 is 300 K.
      • True/false: The temperature of the CO2 is 300 K.
      • True/false: The pressure of the N2 is 100 KPa.
      • True/false: The pressure of the CO2 is 80 kPa.
      • True/false: The volume of the N2 is 0.20 m3.
      • True/false: The volume of the CO2 is 1 m3.
      • True/false: VCO2 =VN2.
      • True/false: vCO2 =vN2.
      • True/false: hmix = 0.20hN2 + 0.80hO2
      • True/false: hbar,mix = 0.20hbar,N2 + 0.80hbar,CO2
      • Now the temperature is increased to T2 and the pressure is increased to P2.
        • True/false: sbar,mix,2 - sbar,mix,1= 0.20[s0bar,N2,2(T2) - s0bar,N2,1(T1)] + 0.80[s0bar,CO2,2(T2) - s0bar,CO2,1(T1)]
        • True/false: sbar,mix,2 - sbar,mix,1= 0.20[s0bar,N2,2(T2) - s0bar,N2,1(T1) - Rbarln(P2/P1)] + 0.80[s0bar,CO2,2(T2) - s0bar,CO2,1(T1) - Rbarln(P2/P1)]
        • True/false: sbar,mix,2 - sbar,mix,1= 0.20[s0bar,N2,2(T2) - s0bar,N2,1(T1) - Rbarln(0.20P2/0.20P1)] + 0.80[s0bar,CO2,2(T2) - s0bar,CO2,1(T1) - Rbarln(0.80P2/0.80P1)]
    • A two-chambered container initially has N2 in one chamber and He in the other chamber. A partition between the chambers is removed so that the N2 and the He mix together. The system is kept at constant temperature and constant pressure during the mixing.
      True/false: Since the two chambers taken together make up a closed system and s = s(T,P), the entropy of the system remains contant.
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    Week 8

    • Consider a moist air mixture at Tdb,1 and φ1 < 100%. The temperature is lowered to Tdb,2 > Tdew,2 at constant total pressure. What happens to the relative humidity?
      • It increases.
      • It remains about the same.
      • It decreases.
      • In sufficient info to determine.
    • Consider a moist air mixture at Tdb,1 and φ1 < 100%. The temperature is lowered to Tdb,2 > Tdew,2 at constant total pressure. What happens to the humidity ratio?
      • It increases.
      • It remains about the same.
      • It decreases.
      • In sufficient info to determine.
    • Consider a moist air mixture at Tdb,1 and φ1 < 100%. The total pressure is lowered to P2 at constant temperature. What happens to the relative humidity?
      • It increases.
      • It remains about the same.
      • It decreases.
      • In sufficient info to determine.
    • Consider a moist air mixture at Tdb,1 and φ1 < 100%. The total pressure is lowered to P2 at constant temperature. What happens to the humidity ratio?
      • It increases.
      • It remains about the same.
      • It decreases.
      • In sufficient info to determine.
    • Explain what is meant by "adiabatic saturation temperature" using layperson's language.
    • Explain how adding moisture to air can lower its temperature using layperson's language.
    • When writing energy balances for pyschrometic systems we often only use the mass flow rates of dry air. How are the energies of the water vapor taken into account, then?
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    Weeks 9 & 10

    • What is meant by complete combustion?
    • In combustion what is meant by the equivalance ratio?
    • The most common model for dry air in combustion requires ______ moles of N2 for every mole of O2.
    • What is the enthalpy of formation of N2?
    • True/false: The enthalpy of combustion for CH4 is h0f,CO2 + h0f,H2O - h0f,CH4 - h0f,O2.
    • True/false: The enthalpy of combustion for CH4 is h0f,CO2 + 2h0f,H2O - h0f,CH4 - 2h0f,O2.
    • What is adiabatic flame temperature?
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