In graduate school at the University of Maryland, I was responsible for designing and testing a prototype CO2 heat pump water heater. This is a device that pumps heat from the ambient air to a water tank, using CO2 as the heat transfer fluid. It is several times more efficient than a standard electric water heater. An electric water heater has an efficiency around 100%. Just about all of the electric energy that is input to the device is delivered to the water, using a resistive coil. It's very simple to control and to understand, and the output is very constant. On the other hand, the heat pump water heater requires electric energy only run a compressor. The heat transfer fluid (CO2) flows in a cycle through the compressor, then through a "gas cooler" where the high temperature, high pressure gas is cooled by the water from the tank (thereby heating the water. High pressure, medium temperature CO2 then passes through an expansion valve, where it drops to a lower pressure and temperature, and becomes a mixture of vapor and liquid at a cold temperature. It is then sent through an evaporator, where the ambient air is used to evaporate the liquid CO2, putting it back in a vapor form that can then re-enter the compressor. Many times more heat energy is released to the water than was required in the form of electrical energy to run the compressor. The energy efficiency of the system is defined as a Coefficient of Performance, or COP, that is the ratio of useful heat energy delivered to the water (the output) divided by the required electrical energy for the compressor (the input). An immediate thought that might come to mind is that this seems to violate conservation of energy. It doesn't though. The heat input to the CO2 in the evaporator plus the electrical input from the compressor balances the heat released from the CO2 in the gas cooler.
Unlike the electric resistance heater, the heat pump water heater is a rather complex system. The COP depends on a range of factors , principally the temperature of the ambient air, the temperature of the water entering the gas cooler, the CO2 charge (or the amount of CO2 in the system, and the speed of the compressor. These four variables are more or less out of the control of the researcher (me!) running the experiments. There were two "levers" that I could play with, however, to adjust the operation of the system, and thereby affect the COP. These were two valves - one controlling the expansion valve orifice opening, and one controlling the water flow rate. The expansion valve orifice opening controls two things simultaneously - the flow rate of CO2 and the difference between the high and low side temperatures and pressures. A tighter expansion valve opening means a slower flow, but higher temperatures and pressures on the gas cooler side of the system and lower temperatures and pressures on the evaporator side of the system. If the expansion valve is open too much, than the temperature of the CO2 can't get high enough to reliably heat the water, and the COP is very low. When the expansion valve is closed too much, the flow becomes too choked, and there is not a strong enough flow of fluid to maintain a high heat transfer rate, and the compressor requires more and more energy to function. Hence the COP is also low at this point. Somewhere in between there is an optimum point, where these countervailing influences are balanced and the COP is maximized. The graph below demonstrates this effect during steady state conditions (i.e. when the system has had a long enough time to settle to a constant rate of operation).
What this graph does not show, however, is the transient effect of changing the expansion valve opening. A transient effect occurs because the CO2 has significant thermal mass. Thus, the mass flow rate is changed almost instantly by adjusting the expansion valve, but the pressures and, especially the temperatures take time to react to the change. Closing the expansion valve causes the COP to drop for a while, before eventually rising again. Opening the expansion valve causes the COP to rise before dropping back to settle to a new equilibrium. At any time when you are controlling the system, you may not know if you are above or below the optimum point in the graph above, in terms of expansion valve opening, so you don’t know if you’re at point 1 or point 2. Note that both point 1 and point 2 have about the same COP. So you don’t know where you’re at exactly, but you’ve decided that your COP is too low and you’re going to do something about it, so you head for the expansion valve. The graph below shows the transient effects of either opening or closing the expansion valve, depending on whether you’re at point 1 or point 2.
If you’re at point 2 and you close the expansion valve, the COP will drop sharply and rise to settle to an even lower COP. This is bad in the short and long term. If you open the expansion valve, your COP will rise quickly and later drop, settling to a higher level than before. This is better in both the short and the long term! But what if you’re at point 1. If you close the expansion valve, the COP will drop for a short while, before eventually climbing to a higher level, closer to the optimum point. This is the smart long term move, but comes at the cost of an even lower COP in the short term. However, if you open the expansion valve at point 1, you can temporarily raise your COP, but at the cost of sabotaging your long-term prospects by moving yourself even farther from the optimum point, and settling to an even lower COP than before.
This is the perfect analogy for what the major world governments are doing with economic policy. We are at point number 1, and we are opening the expansion valve. Only here, the COP is replaced with national and state budgets, and the expansion valve is replaced with the decision to take on more debt or to pay debt back. So if we’re at point 1, and taking on more debt is tantamount to opening the expansion valve further, why would governments do this? Three reasons:
1) It worked in the past! In the past, we were at point 2 (i.e. in an expansionary economy). More debt meant more federal income in the short and the long term. The short term reason why is obvious. More debt means more money now! The long term reason is that the debt was so valuable as an investment instrument that the increased tax revenues as a result of the debt could be expected to more than make up for the cost of repaying the debt in the future. Since we saw this effect happen repeatedly, we worked it into our economic theories and called it a law. The problem is, over time, the repeated application of that solution has moved us from point 2 back over to point 1. As we continue to apply the old remedy, we find that we’re moving to a lower and lower level of federal income. What worked before doesn’t work now because we’re in a new economic regime. We’re on the other side of the optimum point in the heat pump water heater graph.
2) Government officials are elected to relatively short terms and are more interested, generally, in highlighting economic gains on the timeframe of a few years. If the settling time for federal income is a decade, they have no incentive to apply the right corrective action, and instead continue to pull the lever in the wrong direction in order to maximize short term gain. This means more stimulus programs (read debt) to get the economy moving! Interestingly, publicly traded companies have the same sort of incentive system. Shareholders, who are increasingly in the game for the short term demand maximization of short term profits. From this analogy, it isn’t hard to imagine why short term profits can often be at the expense of long term profits. BP is a great example. To maximize profits, it cut a lot of corners with it well drilling, and will now be facing much lower long-term profits because of its cleanup obligations.
3) Here the analogy breaks down, but what if you knew the economy would enter a death spiral (by which I mean positive feedback loops set in that lead to rapid collapse of the financial system) if federal revenue dropped below $1 trillion. You are currently at 1.1 trillion and falling. Thus there is no way to effectively pay back the debt (since this might say, temporatily bring the revenue down to 900 billion, which is in death spiral territory). Thus the only way to survive is to “extend and pretend” by taking on even more debt, perhaps temporarily propping the federal revenue back to 1.2 or 1.3 trillion. The sad truth is that this might extend things a little bit, but it just means a higher degree of pain when the music stops.
If the real reason is truly reason #3, then we are truly screwed, because it is past a point of no return. There is no way out from reason #3 besides financial insolvency, debt default, massive deflation through a collapse in the money supply (or inflation through government printing of money on a massive scale).
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