Download I. POLYTROPIC RELATIONS (25 points)

ME 433
THERMODYNAMICS REVIEW
NAME:
Work individually – use only your text/notes - limit total effort to 180 minutes
I.
POLYTROPIC RELATIONS (25 points)
400 ml of air at standard conditions (25 C, 1 atm) is compressed adiabatically and
reversibly while its volume is reduced by a factor of ten. Assume that this occurs
in a piston/cylinder apparatus and that the ratio of Cp/Cv for air is 1.4 throughout
the entire process.
(i) If the cylinder has a bore of 100 mm, what is the gap between the piston and
cylinder head at the end of the compression process? (watch unit conversions)
(ii) What is the final temperature?
(iii) What is the final pressure?
(iv) What heat transfer occurs during this process?
(iv) What work transfer occurs during this process?
II.
PROCESS & CYCLE MODELING (25 points)
(i)
Sketch the following processes that make up a thermodynamic cycle using data in
the table below. Show pressure-volume (P-V) AND temperature-entropy (T-S)
diagrams. Clearly label the starting and ending points for each process. Assume
ideal gas behavior.
(ii)
Give the sign of the work, heat, and change in internal energy for each process as
well as the entire cycle. Use a back side to explain reasoning for your decisions.
Process
W
Q
U
1-2 isentropic compression
2-3 isochoric heat addition
3-4 isobaric heat addition
4-5 reversible, adiabatic expansion
5-1 isochoric heat rejection
ENTIRE CYCLE (1-2-3-4-5-1)
(iii)
Explain/demonstrate how to use cycle information from only the TS diagram in
part (i) to obtain an estimate of cycle efficiency. Use the back side/extra page.
III.
CYCLE PERFORMANCE ANALYSIS (25 points)
Assume that the Stirling engine (operating at Carnot cycle efficiency) produces 20 kW of
shaft power. The engine absorbs thermal energy at 927 C and rejects thermal energy at
27 C. Assume a fuel with heating value of 42 MJ/kgfuel is burned to supply energy from
the high temperature reservoir.
(i) What is the thermal efficiency of the engine?
(ii) What mass flow rate of fuel is required?
(iii)What is the rate at which heat is rejected in the engine exhaust?
IV.
REACTION BALANCING & AIR/FUEL RATIOS (25 points)
Methanol (CH3OH) is combusted with air which is composed of 21% oxygen and 79%
nitrogen (e.g. for every mol of O2 there are 3.76 mols of N2). Assume that combustion is
complete and occurs under stoichiometric conditions (e.g. the only products of this
reaction are CO2, H2O, and N2).
(i)
Write a balanced reaction for stoichiometric methanol/air combustion.
(ii)
What is the air/fuel ratio for stoichiometric methanol/air combustion on
a molar basis? Carefully outline your solution path and validate your results.
(iii)
What is the air/fuel ratio for stoichiometric methanol/air combustion on
a mass basis? Carefully outline your solution path and validate your results.
Atom
C
H
O
N
(iv)
Molar Mass (g/mol)
12
1
16
14
For methane, the stoichiometric air/fuel ratio is ~17:1 on a mass basis. For
an engine with fixed displacement operating under stoichiometric conditions at
atmospheric pressure, would you expect the mass flow rate of methanol to be
larger or smaller than methane in the same engine (same compression ratio,
engine speed, and inlet conditions)? Why?