Exam (elaborations)

Mtx 311 2017 exam memorandum

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Course
MTX 311 (MTX311)

Institution
University Of Pretoria (UP)

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Thermodynamics MTX 311

Exam: June 2017

Examiner

Dr AS Lexmond (University of Pretoria)

Instructions

1 Time: 180 min.
2 Full marks: 100
3 Neatness saves you points, especially when only part of the question is correct.
4 Give the equations before you start filling in numbers; for the questions marked with an
*, also give a short but clear solution strategy
5 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”, as well as any other notes or books you like
6 use a reference temperature and pressure of T0=25°C, P0=1 bar
7 Note that the amount of marks for a question represents how important I find it, not the
time it will cost you to solve it.

1) Hydrazine (N2H4) is a substance that is regularly used as a rocket fuel, where it is combusted with
stoichiometric oxygen.
1A (5pts) Give the reaction equation of the combustion of hydrazine with 50% excess air.
1B (5pts) what is the dew point (at 1 bar total pressure) of the gas mixture that is formed?

Of course, you fist solve the reaction with stoichiometric oxygen only. For this, you make a table:
in out
in out N H O N H O
1 N2H4 2 4
1 O2 2
1 N2 2
2 H2O 4 2
Reaction with oxygen: N2H4+O2 N2 +2H2O

Now you add nitrogen and the excess air:
Reaction with st. air: N2H4+(O2+3.76N2) 2H2O +(1+3.76)N2
Reaction with 50% excess air: N2H4+1.5(O2+3.76N2) 2H2O +(1+5.64)N2 +0.5O2

1B) The dew point is the temperature at which condensation starts. Since we are dealing with a
mixture of ideal gases, condensation starts when the partial pressure of one of the components

, (usually water) reaches the saturation pressure. The gas mixture that is formed consists of water
vapour(2), nitrogen(6.64) and oxygen (0.5). Obviously , water vapour is the fist components to
condense. The reaction equation gives molar ratio’s: use this to determine mole fractions, and
calculate partial pressure of water vapour. (you could make a table for this, but this is so simple that
you don’t really have to). When you have the partial pressure of water vapour, interpolate Tsat from
table B1.1 or 1.2 to get the dew point.

n Y
N2 6.64 72.65%
O2 0.5 5.47%
H2O 2 21.88%
tot 9.14

PH2O=yPtot=21.88*100=21.88kPa

P T
20 60.06 °C
25 64.97 °C
21.88

x 0.376
T 61.90616 °C
Tdew=61.9°C

2) One of the interesting properties of hydrazine is that it is very instable; even without oxygen,
hydrazine can decompose, forming one nitrogen molecule and two hydrogen molecules:
N2H4N2 +2H2. This reaction releases quite a lot of energy; when hydrazine (a liquid at room
temperature) decomposes, it forms a gas mixture of 650°C and 80 bar. (You can assume that the
mixture behaves as an ideal gas.)
In case of a combustion system malfunction of the rocket, the nitrogen-hydrogen mixture can also
be used for propulsion. You can assume that the gas mixture leaves the rocket at four times the
speed of sound.

2A (10pts) what is the k-value of the nitrogen-hydrogen mixture? (at room temperature)

No matter whether we are dealing with a pure gas or a gas mixture,here is only ONE way to
determine the k-value:
k=Cp/Cv (=Cp/(Cp-R)
Since decomposition of hydrazine forms a gas mixture, we have to determine Cp and Cv (or Cp and R)
of the mixture. To do this, we first determine mass fractions of nitrogen and hydrogen after which we
can determine mass fraction averaged Cv and Cp(to calculate k). A small complication is that the
reaction gives the MOLAR ratio’s, so first we convert molar ratio’s (y) to mass ratio’s (c). Obviously,
the easiest way to do this is make a table:

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