Thermodynamics MTX311 exam 2019 worked out solutions. The memorandum has solutions are 100% correct including alternative working methods. The solutions are done in a step by step matter
QUESTION 1 [20]
A 1-m3 insulated tank contains air at 1 MPa, 560 K. The tank is now discharged through a
small convergent nozzle to the atmosphere at 100 kPa. Find the initial mass flow rate out of
the tank if the nozzle has an exit area of 2 × 10-5 m2.
P0 = 1 MPa ✓ The nozzle in converging which means M ≤ 1.
T0 = 560 K ✓
The back pressure is 100 kPa which means
✓
But the highest possible pressure ratio in a converging nozzle, where M = 1, is
✓ (OR PB = 528.3kPa)
Which means the nozzle is choked (M = 1) ✓✓
Because ✓(check)
TE = T* = 0.8333 × 560 = 466.7 K ✓
✓✓ ✓✓
✓✓ ✓✓ (OR ρ = 3.94kg/m3)
✓✓ ✓✓
OR (6)
, QUESTION 2 AND 3 [50]
Use T0=300K, P0=100kPa
Currently, producing large amounts of renewable energy at affordable cost is no longer a significant
challenge; solar and wind electrical energy can be produced affordably and at a large scale in South
Africa. Storing the energy so that you can use it when you need it, and not when the wind is blowing
or the sun is shining is, however, a large challenge that has not been completely resolved yet. A
possible solution is to convert the electricity into hydrogen and store the hydrogen. When electricity
is needed, the hydrogen can be converted into electricity using fuel cells. Typical fuel cell efficiencies
(40-65%) are not good enough for energy storage purposes; an efficiency of about 80% for
converting hydrogen back into electricity is needed. To achieve higher efficiencies, fuel cells with co-
generation are needed. A PFD of such a process is given in fig. 2; process flow properties and
equipment properties are given in tables 1 and 2.
1MW
potassium carbonate fuel cell 6
hydrogen in
15g/s 1 4
B
3 C
650°C
A 640 kW
5
2
10
D 9
H
E
8 6
F G
11 7
fig. 2 PFD of energy conversion plant with co-generation fuel cell technology
Table 1 average stteady state process flow properties Table 2 unit power production and
m (kg/s) T(K) P (kPa) H (kW) Ψ (kW) consumption
1 hydrogen feed 0.015 300 1000 1800 1850 name W (kW)
2 air feed 0.55 300 100 0 0 A cooled compressor 120
3 compressed air 0.55 350 1000 26 104.6 B fuel cell 1000
4 hot air 0.57 920 975 322 249 C Brayton turbine 215
5 expanded air 0.57 480 100 105.6 25 D main heat exchanger
6 waste air to chimney 0.57 340 100 20.8 1.3 E Rankine turbine 240
7 pump feed 0.21 325 20 22.1 0 F condenser
8 high pressure water 0.21 325 4100 23 0.8 G pump 1
9 preheated water 0.21 425 4050 130.4 17.4 H preheater
10 turbine feed steam 0.21 875 4000 771.6 311.4
11 low pressure steam 0.21 335 20 528.2 51.9
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