Combined Cycle (CC) Natural Gas Power: Cheap natural gas (mostly from fracking and similar extraction techniques) and CC gas plants are one of the primary reasons that US carbon emissions peaked in ∼2010 and has been declining. Here, natural gas powers a Brayton cycle turbine, and the exhaust from that turbine is then fed into a steam generator to run a Rankine cycle turbine. a) The high temperature in the Brayton cycle turbine is 1500K. The exhaust for the Brayton cycle exits at about 850K. What is the maximum efficiency that you could expect from a heat engine operating between these two temperature extremes? b) A heat exchanger is able to deliver the Brayton cycle exhaust to a Rankine (steam) cycle. The the final outgoing temperature from this steam cycle is 325K. What is the maximum efficiency that you could expect to achieve operating between the high temperature from the Brayton cycle and the low temperature from the Rankine cycle? (That is, what is the theoretical max efficiency of the combined cycle?) c) In reality, the single-cycle Brayton plants only achieve about 33% efficiency. When the sun doesn’t shine, solar power is backed up by single-cycle gas plants (the time required to start a boiler to run a combined cycle plant is too long). Suppose that, in order to back up a solar plant, you need to deliver one gigawatt (109 W) of work to the electric grid for 104 seconds (about three hours) after the sun sets using a single cycle plant. What is the total amount of energy you must expend (Qin) to deliver this energy to the electric grid as work? d) The best CC gas plants achieve roughly 60% efficiency. If you were to input the same amount of energy as used in the previous part (the same Qin) to deliver one gigawatt of work with a CC plant, how many seconds of operation could you achieve? From this answer, and your result from the previous question, how many seconds of sunlight (at 1GW) must you capture before you break even in terms of the total input energy? (Assume that the equivalent thermal efficiency of solar is 100%, which it is not.)

3) Combined Cycle (CC) Natural Gas Power: Cheap natural gas (mostly from
fracking and similar extraction techniques) and CC gas plants are one of the
primary reasons that US carbon emissions peaked in ∼2010 and has been declining. Here, natural gas powers a Brayton cycle turbine, and the exhaust
from that turbine is then fed into a steam generator to run a Rankine cycle
turbine.
a) The high temperature in the Brayton cycle turbine is 1500K. The exhaust for the Brayton
cycle exits at about 850K. What is the maximum efficiency that you could expect from a
heat engine operating between these two temperature extremes?

b) A heat exchanger is able to deliver the Brayton cycle exhaust to a Rankine (steam) cycle.
The the final outgoing temperature from this steam cycle is 325K. What is the maximum
efficiency that you could expect to achieve operating between the high temperature from
the Brayton cycle and the low temperature from the Rankine cycle? (That is, what is the
theoretical max efficiency of the combined cycle?)

c) In reality, the single-cycle Brayton plants only achieve about 33% efficiency. When the
sun doesn’t shine, solar power is backed up by single-cycle gas plants (the time required to
start a boiler to run a combined cycle plant is too long). Suppose that, in order to back
up a solar plant, you need to deliver one gigawatt (109 W) of work to the electric grid for
104
seconds (about three hours) after the sun sets using a single cycle plant. What is the
total amount of energy you must expend (Qin) to deliver this energy to the electric grid as
work?
d) The best CC gas plants achieve roughly 60% efficiency. If you were to input the same
amount of energy as used in the previous part (the same Qin) to deliver one gigawatt of
work with a CC plant, how many seconds of operation could you achieve? From this answer,
and your result from the previous question, how many seconds of sunlight (at 1GW) must
you capture before you break even in terms of the total input energy? (Assume that the
equivalent thermal efficiency of solar is 100%, which it is not.)