GEOS / ENST / ENSC 2100 Problem set #10 Due: Tues. Mar 2

Transcription

1 GEOS / ENST / ENSC 2100 Problem set #10 Due: Tues. Mar 2 Problem 1: Power plants Read the reading from the Brian Hayes book Infrastructure on fossil- fueled power plants and comment on something interesting. If you went on the field trip, relate it to what you saw. Problem 2: Energy transformation technologies and efficiencies The 17 th - 18 th century energy dilemma included the problem that people could not transform heat to work. In modern life, we now have technologies to transform almost every form of energy to every other form. In class we filled out a grid of energy transformations, writing down technologies people have invented (or natural processes) that transform energy FROM the type on the vertical label and TO the form on the horizontal label. The diagonal boxes represent ways of moving or storing energy. In this problem you ll use the grid on the web page to trace out the chain of energy transformations involved in some aspects of your everyday life. For each transformation in the problem below, you ll print out a grid and draw the transformations on it. You ll also book- keep the energy losses that occur during that chain. The table on the following page (from Smil) gives conversion efficiencies for many common transformations. It gives nearly all the info you need, but here is some additional info. First, Smil doesn t book- keep the losses in electricity transmission lines. In the U.S., those are on average 7%, i.e. electricity transmission and distribution is about 93% efficient. Smil doesn t list an efficiency for microwaves (eà h); those are typically ~65%, a number consistent with the findings of those students who did the experiment themselves. This chart pre- dates the invention of the commercial LED bulb; good modern LEDs are up to 20% efficient. For solar photovoltaics, the chart lists the best as 20-30% efficient but that s not a reasonable number; commercial PV panels are more like 15%. Smil lists photosynthetic efficiencies for plants as 1-2% max but remember that the efficiency for plant food edible by humans is less, more like 0.5%. Finally, it s interesting to see that Smil assumes that conversion of food à meat in animals is 30-35% efficient. We saw in class and prior problem sets that a cow is more like 10%, but a modern chicken is 50% efficient. Unless told otherwise, assume for now that all electricity is produced by burning some fossil fuel and spinning a steam or gas turbine. For the problems below (other than those in italics), you should turn in 1) a printout of the technology grid numbering (or otherwise marking) the progression of transformations, and 2) a calculation of the net efficiency of the entire process. For transformations that start with some kind of plant matter or fossil fuel, ignore the efficiency of converting sunlight to chemical energy in plants start with the fuel. A. Cooking with a gas stove B. Cooking with an electric stove C. Cooking with a microwave D. Heating your house with a furnace

2 E. Heating your house with a space heater F. Heating your house with a heat pump with COP = 3.5. Here you can assume that the rated COP includes the losses of the electric motor that drives the compressor used in the heat pump (i.e. don t include the small- electric- motor transformation; it s already wrapped into the rated COP). G. At what COP would a heat pump use the same primary energy as a furnace? You examined this issue PS 8, but use this more formal representation to evaluate the question more carefully. H. Your answers to D and E should be quite different because of the inefficiency of producing electricity. That inefficiency must affect the electricity price. Use what you learned above to predict what you d expect the price of electricity to be relative to the price of natural gas. Then look up the wholesale (not retail) prices of electricity and natural gas, put them in common units (a good unit is cents/kwh), compare and discuss. (For electricity, the wholesale price is that paid to the power plant; the retail price is what the customer gets charged.) Make sure to state your sources.) One kwh is the energy consumed at a rate of 1000 W for one hour (3600 s), i.e. 3.6 MJ. I. Look up the retail price of electricity for a residential customer like yourself and compare to the wholesale price. J. Lighting your house with candles K. Lighting your house with electricity- powered standard incandescent lightbulbs. L. Lighting your house with electricity- powered modern LED bulbs M. Many techno- optimist environmental groups believe that the agriculture of the future involves growing our food indoors under artificial lights (LEDs), in vertical farms. The argument is that this will save energy, since it allows food to be grown locally, and that it saves on land, since food can be grown in multi- story buildings. Fill out the chart for the chain of transformations in converting chemical energy in fossil fuel into chemical energy in food. N. Using your answer above, if you were to produce all your 100 W of food in vertical farms, what primary power consumption would that require? How would this compare to your present- day 10,000 W of total power use? O. Advocates of vertical farms claim that the electricity required for lighting could be produced by renewables. The most efficient of the renewable electricity- generating technologies is solar PV. Fill out the chart for the transformations needed to convert the radiation energy in sunlight into radiation energy from LED lights in your vertical farm. What is the total efficiency? P. We presently use a bit over 10% of the Earth s land surface area for growing crops. What fraction of land surface area would be required for solar PV panels to produce electricity to light the lights to grow that food indoors instead? Is this feasible? (Note try to figure out how to answer this question in a simple elegant way, without multiplying by the surface area of the Earth.) Q. (Optional) How much land would you need if you made your electricity from biofuels instead?

3 From V. Smil

4 Problem 3: Vertical farming : analysis using costs Growing food indoors under artificial light is not only touted by some environmental- minded groups, it is actually happening: see the articles below about a facility in New Jersey to grow kale: newark- a- vertical- indoor- farm- helps- anchor- an- areas- revival.html?ref=nyregion An earlier article is here: 30/aerofarms- plans- aeroponic- farm- in- newark- to- grow- leafy- greens. In the previous problem, you evaluated the efficiency of the chain of transformations involved: radiation energy à chemical energy à kinetic energy à electrical energy à radiation energy In this problem you ll examine feasibility using another metric, cost. Generally cost and energy scale well together, because energy is not free. If a process requires more energy, it costs more. And you know the cost of electricity (you looked it up in Problem 1). That cost reflects all the losses and inefficiencies that went into making the electricity, so lets you ignore the upstream part of the energy conversion chain. Cost should also provide some immediate intuition about the high energy requirements for growing food (or any plant) under artificial lights. There is only one agricultural product in the U.S. that is routinely grown indoors under artificial lights marijuana. And marijuana grow houses are often identified by their suspiciously high electricity bills: bust- shines- light- on- utilities/article_f63a8bed- 9a aaef- 99f7eb0f71f0.html In this problem you ll be using the metric of cost per energy content: both the cost per energy inputs to grow food, and the cost per chemical energy in that food. The most reasonable units, to keep the values intuitively understandable, are the same ones that electricity is sold in: cents/kwh (or $/kwh when that seems more appropriate). A. First, consider the efficiency of turning electricity into chemical energy in the kale being grown in New Jersey. As you did in Problem 1, you just multiply through the energy conversion chain (electricity à radiation à chemical). In this case, because you eat all the kale (it s just a leaf), you can assume a photosynthetic efficiency more like 1%. B. Invert your value in A to get a factor that relates the electrical energy used for lights in an indoor farm to the chemical energy of food produced. Discuss. Remember that it seemed shocking that conventional farming required as much energy in fertilizer as it produced in food: a factor of 1! (Note: for a truly fair comparison, you would use your answer of M instead, which would multiply your factor here by about another x3 to account for the fossil fuel required to make electricity.) C. Now multiply the factor of B by the (retail) price of electricity (cents/kwh_electricity) to get the cost of electricity required per kwh of chemical energy in kale produced. You then want to figure out how much that electricity expense would drive up the price of kale D. The first step is to find the cost of kale in $ or cents/gram. For this problem, consider ordinary kale, not the fancier baby- kale kind. The right comparison would be to the wholesale price, but that s hard to find online, so we ll stick to the retail price. You can find price information from the USDA here: products/fruit- and- vegetable- prices.aspx but any source is OK. Convert units as needed.

5 E. Then turn that price per mass into a price per energy content. Kale is mostly water, so you need to do some searching here rather than just using the metric of 4kCal/gram for carbohydrates. Wikipedia helpfully tells you its energy content per mass: Write down the kcal/gram of kale. Then use this factor to turn your value in D into a price in units of $ per kwh. F. Compare E to C: by what fraction would you have to increase the price of kale if you grew it under artificial lights, so that you could recover the additional cost of electricity? Discuss. G. Optional: What fraction of kale is water? Convert your kale cost of E into a cost per dry gram. H. Optional: Even if you can t realistically have a business selling ordinary kale grown under lights, you might have a more plausible product in the already- expensive market for fancy overpriced salad greens sold to Whole- Foods- type shoppers with plentiful disposable income. Look up the cost of fancy salad greens, calculate their cost/energy content (repeat D and E), and compare to the additional cost of electricity required to grow them under lights (repeat F). I. Optional: Find an actual price for indoor- grown salad greens, and compare to the cost you estimated for electricity to grow them. You should find the prices have been raised by enough that producers can stay in business. Note it used to be possible to go to Whole Foods in Chicago to find indoor- grown greens and look at their prices, but the company producing them has in this case (and thankfully for the planet) gone out of business due to high operating costs : farmedhere- closing biz story.html You can also evaluate the market for the one product grown under artificial lights. Since pot is now quasi- legal in many states, you d expect its price may roughly reflect production costs (and no longer be inflated to include the additional costs incurred in running an illegal activity). The price should still be high enough, though, to pay for the electricity required to produce it. J. Optional: Look up the cost of marijuana (you can find it in $/gram). You can assume the mass is a dry mass, so compare it to the cost per dry mass of (ordinary, outdoor- farmed) kale in part G. You would expect that marijuana should be more expensive than an everyday vegetable. Is it? K. Optional: Now calculate the cost of marijuana per energy content in $/kwh. There seems to be no nutritional information released by the USDA (unsurprisingly), so just apply the standard metric of 4kCal/g for any carbohydrate. Compare your result to the electricity cost in C: what fraction of the cost of marijuana is the electricity required to grow it indoors?