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Thermodynamics MTX 311Semester test 1: March 2015
Examiner
Dr AS Lexmond (University of Pretoria)
Instructions
1 Time: 90 min.
2 Answer all the questions
3 Full marks: 100
4 Give the equations before you start filling in numbers; for the questions marked with an
*, also give a short but clear solution strategy. If there is no strategy, I will give full mark
(answer correct) on 0 points (no strategy)
5 It is YOUR responsibility to ensure that I understand your calculations. Neatness saves
you points, especially when only part of the question is correct.
6 This semester test is open book. You are allowed to take fundamentals of
thermodynamics (7th or 8th edition), non-ideal gas hand-out, one page, A4, with your
own notes (both sides) and all the material from the click-up page “lectures”
Question 1
For dry climates, evaporative air coolers are a good alternative to air conditioners. In such an air
cooler, 100 g/s (of dry air) of an air-water vapour mixture 40°C, 1bar, 20% relative humidity, is
cooled down by nebulizing liquid water in it. Evaporation of the water results in cooling.
15pt 1A) what is the lowest temperature that we can achieve with this system?
15pt 1B)* How much water do we have to feed into the cooler to achieve a mixture temperature of
25°C?
Question 2
20pt 2A)* Combustion of hydrogen can result in very high temperatures. To avoid thermal damage
to a combustor, hydrogen (25°C, 1 bar) is combusted with a lot of excess air (25°C, 1 bar) to keep the
temperature in an adiabatic reactor below 1000K. How much excess air has to be added exactly?
15pt 2B)* what is the mixture Cp of a stoichiometric mixture of hydrogen and Oxygen?
Question 3
Micro-turbines differ from “normal” large turbines in one important way: the assumption that the
turbine is adiabatic is not valid anymore. For rally small turbines, the assumption of an isothermal
turbine is much better. An isothermal reversible microturbine is fed with 1g/s of ethylene at 25°C,
100 bar. The pressure at the turbine outlet is 2 bar.
20pt 3A* How much is the change in entropy?
We must find the heat transfer to allow the design the heat transfer fins on the isothermal
microturbine.
15pt 3B* Use the change in entropy to calculate the heat flux into the micro-turbine. (If you failed in
3A, you can assume an entropy change of 1 W/K). Is heat going into the turbine or coming out?
, 15pt 1A) what is the lowest temperature that we can achieve with this system?
This is typically the type of question that is VERY easy to answer with the psychrometric chart. In a
psychrometric chart, the enthalpy of liquid water is 0kJ/kg. Addition of liquid water is therefore a
CONSTANT ENTHALPY process. You reach the lowest temperature by evaporating water until the
relative humidity is 100%. This is the wet bulb temperature. Read off from the phychrometric chart
(solid line): Twet bulb =22C
How much water do we have to feed into the cooler to achieve a mixture temperature of 25°C?
15pt 1B)* How much water do we have to feed into the cooler to achieve a mixture temperature of
25°C?
In this question, we add and evaporate liquid water which until the temperature is 25°C. Like in Q1A,
this is a constant enthalpy process, but now we stop at T=25°C (and not at φ=100%)
Strategy:
1) use psychrometric chart to get humidity ratio in and out
2) get water consumption from humidity ratio increase and dry air mass flow rate
1: ω1=0.0093, ω2=0.0158
Δω=0.0158-0.0093=0.0065
mevap=mair Δω=100∙0.0065=0.65 g/s
20pt 2A)* Combustion of hydrogen can result in very high temperatures. To avoid thermal damage
to a combustor, hydrogen (25°C, 1 bar) is combusted with a lot of excess air (25°C, 1 bar) to keep the
temperature in an adiabatic reactor below 1000K. How much excess air has to be added exactly?
Strategy:
1) Solve heat balance: split process in 3: combustion with stoichiometric air, heating of “100%
theoretical air–reaction products” to 1000K and heating of excess air to 1000K
2) Solve reaction equation
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