## Transcribed Text

1. Enthalpies of reaction and heating
a)
You need to haul your fuel and store it so that the quantity of most interest to you is the
number of kJ you get for combusting a fixed weight of it. Determine whether gasoline
(octane), liquefied natural gas (CH4(1)) or biofuel (ethanol) is your preference giving the
number of kJ per kg you can generate.
b) You would like to heat the air (assume it is all nitrogen and oxygen at 295 K) in a well
insulated room that is 4x 6 X 3 cubic meters in size by 5 degrees Celsius using the heat
from a combustion reaction. Assuming you can transfer the heat of reaction perfectly into
the air, how much of your fuel will you need? (Note: For the purposes of this problem,
you should make the realistic assumption that the pressure is constant at 1 atm. Also,
please
use
a
simple
estimate
for
the
specific
heats
of
oxygen
and
nitrogen
that
neglects
vibrational excitation rather than doing complex calculations.)
c) Suppose we tried a more sophisticated model of the specific heat accounting for
vibrational modes. Would I calculate that I need to use more fuel or less (explain how
you know)?
d) Suppose that all of the oxygen in the room happened to be composed of the 180 isotope
rather than the common isotope? Would that make the computed amount of fuel needed
increase, decrease or stay the same? Explain your answer.
2. Engine efficiencies and useful work
We defined efficiency of an engine by the ratio of work done in a full cycle on a P-V plot to
the heat put in during the expansion. I asserted that the Carnot cycle (isothermal expansion at
Th followed by adiabatic expansion followed by isothermal compression at T1 followed by
adiabatic compression) produces the most efficient possible engine for a given amount of
expansion V min
V
max.
a) You are interested in the following alternative way to expand which is to isothermally at
In expand all the way to Vmax and then lower the temperature to T1. while holding the
system at constant volume. After that, you do the reverse and isothermally contract all the
way to Vmin and raise the temperature while holding the volume constant. Calculate the
efficiency for the alternative process and prove that it is lower than the Carnot engine
efficiency.
b)
Explain this result physically - in other words, why did you need to either put in more
energy or why did you get out less work?
Pressure
Solid line = Carnot
Solid plus dashed = alternative
Vmin
Vmax
Volume

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