Heating Up the Planet – A Fresh Hot Look at Global Warming

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Heating Up the Planet – A Fresh Hot Look at Global Warming

https://doi.org/10.21203/rs.3.rs-1972419/v1

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Global warming is an inescapable phenomenon that seems to be unquestionably linked with Human activity, in particular with the way Humanity uses energy, and constitutes one of the most important challenges we are facing in the near future.

The occurrence of global warming is being linked to the emissions of gases with a greenhouse effect, that is, gases that can trap heat in the atmosphere and, thus, induce an imbalance between the energy the Earth receives and the one that it is able to emit back into space. This imbalance induces an accumulation that is credited as responsible for the warming of the atmosphere.

In this paper, we take a different view, based on a thermodynamic analysis, of the overall world’s energy production/consumption system and raise the issue that the warming of the atmosphere is likely to be affected by the energy system in more ways than this imbalance between energy intake and energy release due to the emissions of greenhouse gases and that it may be directly influenced by the generation and use of energy itself. The main conclusion that we reach from our calculations is that the amount of energy that is currently being produced on a global scale can actually make a significant contribution, if not the major contribution, to the current increase in atmospheric temperature.

Global Warming

Exothermic Reactions

Heat of Reaction

Enthalpy Balance

Global warming is a very important issue that must be urgently addressed. The rise in average temperature is well documented and it seems to be inextricably linked to human activity. As indicated in the 2014 IPCC report “Warming of the climate system is unequivocal, and since the 1950s, many of the observed changes are unprecedented over decades to millennia” (Stocker, et al. 2013). This increase in global average temperature is associated with the accumulation of thermal energy in the atmosphere and its surroundings, the ocean and other water bodies, glaciers, etc.

The impact of human activities on the environment has been increasing and takes on many different forms. Human activities collect resources from the environment, which causes a significant disturbance in the natural equilibrium, but also causes emissions, both in terms of material emissions, including waste and greenhouse gases, but also energy emissions. For a long time, material disturbances were considered to be minor, in relation to the size of the natural environment, but this has changed, and material waste management is now a requirement for all human activities. Energy emissions have also been the object of interest, but mostly at the local level. The energy emissions correspond to different types of pollution, like sound pollution (Environmental Energy Agency 2020), light pollution (Falchi et al. 2019) and also thermal pollution (Vallero 2019). Energy emissions, which are often defined as “the discharge of heated water into bodies of water” (Posudin 2014) have been associated with environmental disturbances but mostly in terms of the heat released from thermoelectric power plants (Raptis et al. 2016), which can even disturb power production from other power plants (Miara et al. 2018). However, all these studies were only limited to the local impact of the heat released and are limited to the waste heat that is generated in the power plants and that is seen to add to the global warming effects (Liu et al. 2020).

In this paper, we intend to show that the heat emissions generated by human activity, which include but are not limited to energy production/consumption, are capable of having a major impact on global temperatures.

The commonly accepted description of the temperature in the atmosphere is based solely on a global energy budget, considering the energy that Earth receives from the surroundings (the Sun) as an input and the energy that is radiated back into outer space as the output (Archer 2012; Jacobson 2012). It is usually accepted that if a steady-state is to be attained, whereby the energy input and the energy output are the same, the temperature should remain fairly constant. This approach corresponds to a global energy balance and allows the analysis of the energy content of the Earth (and its atmosphere), but it is an incomplete description in terms of the understanding of the change of physical properties like the temperature. Actually, if a system is in a steady-state in terms of energy inputs and outputs, or even if it is an adiabatic condition with no heat exchange with its surroundings, the temperature may be altered due to the different ways the energy distributes itself on the various forms: heat, mechanic, chemical, nuclear, gravitational, etc. This is apparent in our daily life, for example when a gas heater is used to heat up a space.

However, according to the IPCC report, the anthropogenic forcing of climate is only attributed to radiative forcing, associated with the formation of atmospheric species that interfere with radiation absorption and emission (Stocker et al. 2013). The currently most widely accepted theory to explain global warming is the carbon dioxide theory, although alternative views have been put forward that question the weight of carbon dioxide emissions in global warming (Fleming 2018).

However, looking at the global energy balance just in terms of inputs and outputs is only valid, for the purpose of temperature calculation, if no chemical (or nuclear) reactions occur. Earth is a reacting system, where a series of chemical (or nuclear) changes occur, some natural, but more important, some induced by human activity, and most of these reactions involve significant amounts of energy being transformed from one type to another. In fact, chemical compounds have a specific amount of internal energy (U). When a chemical reaction occurs, part of the chemical energy, which can be described by the Gibbs terms in the overall internal energy of a system, will be transformed into (or from) thermal or mechanical energy.

$$U=TS-\text{P}\text{V} + \sum _{all chemical species}{\mu }_{i}{n}_{i}$$

where T, S, P and V stand for temperature, entropy, pressure, and volume respectively, and ${\mu }_{i}{n}_{i}$ is the Gibbs term corresponding to the chemical internal potential of a species i.

At this stage, we should note that, although this discussion will be mainly centred on the energy associated with chemical reactions, as these are currently the major source of energy for human activities, the same applies to the energy associated with nuclear reactions, which are also of paramount importance for the energy supply of our society; a fission reaction will convert energy that is stored inside nuclei into heat when a heavy nucleus is split into two smaller ones. This is also relevant for the analysis of the Earth’s energy budget, and, in the following, whenever we discuss the energy involved in chemical reactions, we should note that the same applies to nuclear reactions or, in fact, to any other way of transforming different forms of energy into thermal energy.

Although thermochemistry is a regular subject in atmosphere thermodynamics textbooks (North and Erukhimova 2009), we have no knowledge of these issues being considered in terms of atmosphere warming evaluation, which is described, for example, by a “Layer Model with Greenhouse Effect” (Archer 2012). The implications of these thermochemical transformations will be our topic in the following discussion.

The temperature effects associated with chemical reactions are often addressed in the context of reaction engineering by using an Enthalpy balance since this thermodynamic potential is more convenient in situations where the mechanical energy associated with the term PV needs not be computed, as is the case of many chemical reactors. In the following, we address the issue of global warming using a similar approach by analysing the global enthalpy balance to the atmosphere. This approach will allow us to estimate temperature variations associated with the chemical transformations behind the production of energy.

Let us consider the entire Earth’s atmosphere and write an enthalpy balance to this system. The atmosphere is composed of gases that, upon temperature changes, will expand or contract. This involves work done against or by gravity (changing the PV term in the internal energy definition) which is not easily computed. Thus, in order to compute the temperature changes, we will consider an enthalpy balance, since enthalpy (H) is defined as

$$H=U+PV=TS + \sum _{all chemicalspecies}{\mu }_{i}{n}_{i}$$

which is also an exact thermodynamic potential and subject to similar conservation laws, as the internal energy.

The enthalpy (${H}_{atmosphere}$) inventory of the Earth’s atmosphere system includes sensible heat, relevant phase change enthalpies, as well as all the chemical (and nuclear) potential energies:

$${H}_{atmosphere}=TS + \sum _{all chemicalspecies}{\mu }_{i}{n}_{i}$$

The Earth’s atmosphere’s total enthalpy will change only due to heat exchanges with the surroundings, which include all the radiation coming from the sun and all the radiation that radiates back into space.

As the discussion is currently centred on the changes induced by human activity, we will assume that, in the absence of this activity, energy fluxes in and out of the atmosphere are the same, which can be seen as the pre-industrial situation.

During the industrial revolution, the major change that occurred was that human activity resorted extensively to the burning of fuels for its activities. This fact, although it did not change the influx or outflux of energy from the Earth, induced a very large release of thermal energy that was previously stored as chemical energy in the fuels that were used, initially coal but later oil, and gas and nuclear fuels. Note that the objective of the use of energy was not only to generate heat but to generate work, that powers the factories; however, all the work that is produced is eventually and inevitably degraded into thermal energy. Thus, even if the overall energy or enthalpy content on Earth does not change, the fact that chemical energy is being converted into heat, according to Eq. 3, is going to produce changes in Earth’s temperature. As we already said, there is a tendency to neglect these emissions as being insignificant in relation to the size of the environment and this is the assumption that we will analyse in the following.

It should also be pointed out that an increase in temperature will also result in an increase in radiation emissions by the earth, increasing energy output, although part of these emissions can, in fact, be retained by greenhouse gases in the atmosphere.

For argument’s sake let us consider, as a simplifying assumption, that the Earth’s atmosphere is in a balanced state, where the amount of energy that is received is exactly matched by the amount of energy that is radiated back to space.

$$\frac{d{H}_{atmosphere}}{dt}=0= \frac{dTS}{dt} + \sum _{all chemical species}{\mu }_{i} \frac{d{n}_{i}}{dt}$$

As per the arguments above this would imply that the temperature would change if some of the energy contained in the chemical energy term is converted to thermal energy. Let us consider a simple example, which is very commonly used in our society to produce electricity, the combustion of coal:

$$C+ {O}_{2} ⟶{CO}_{2}+Heat$$

This reaction involves a decrease in enthalpy of the chemical system, associated with the change of its chemical composition, which is measured by the reaction enthalpy and corresponds to a decrease in the second term on the right-hand side of Eq. 3. If the overall enthalpy of Earth is to remain constant, as per the adiabatic assumption, this decrease will imply that the term TS, i.e., the content of thermal energy, increases thus inducing an increase in the temperature of the system. This reaction is the one that allows us to produce steam in coal power plants. Similar reactions, albeit involving other chemical species, allow us to have a hot bath when we burn natural gas to heat up water or power the engine in a vehicle. This is a clear example that the chemical reactions that are used to produce energy do change the temperature of the surroundings where they are taking place.

As already stated above, this also applies to nuclear energy, where heat is released by the change in the atomic composition of a system, hydropower energy, where potential energy is first converted into kinetic energy (of the water flowing), and ultimately into heat when this kinetic energy is used for other purposes, such as heating our houses. In fact, it can be argued that all the energy that is produced by human society is ultimately transformed into thermal energy – we use the energy that we produce to heat our buildings, which directly produces thermal energy, but we also use the energy to drive our transports, directly producing heat as a by-product in the engines, but also mechanical energy, in the form the kinetic energy of the vehicles. However, even this kinetic energy is ultimately converted into heat due to the resistance to the movement and braking.

In the following, we will assume that all energy that is produced in our society’s energy system will ultimately be converted into thermal energy and, thus, will contribute to the increase in temperature of the atmosphere.

Using this assumption, we can make a preliminary calculation of the effect that the energy production system has on the temperature of the atmosphere, where most of this energy is released.

According to the International Energy Agency’s data, in 2019 the total primary energy that was produced worldwide was 606 EJ (International Energy Agency, 2021).

This is a very large amount of energy that, as discussed above, will ultimately be transformed into thermal energy, partially during the production and transformation stages themselves or, at most, after usage. This amount of energy is released into the environment. Not all, but a very large part of it, will be released into the atmosphere, although part of it may also be directly released into water bodies, as already discussed above (Raptis et al. 2016; Miara et al. 2018), or even the soil.

As a first approach, we will consider that all the energy is released into the atmosphere, either directly, by mechanisms as diverse as the power plants themselves (by their smokestacks and cooling systems), by its usage as heating sources, by resistance losses during electricity transport or by mechanical energy losses, for instance, due to vehicle traffic.

If we assume that this amount of energy is released into the atmosphere, we can estimate the increase in temperature that is originated; again, we are considering that the global enthalpy is constant, i.e., the amount of energy received from the surroundings equals the amount radiated back into space.

To compute the change in temperature we need to know the mass of the atmosphere. The total mass of the atmosphere changes throughout the year, depending on the amount of water vapour that it contains. Several estimates have been made at different times (Verniani 1966; Trenberth and Guillemot 1994; Trenberth and Smith 2005) but they are all very close. Using the estimate published by Trenberth and Smith (2005), the total mass of the atmosphere is around 5.1352 × 10¹⁸ kg (neglecting the water vapour content) or 5.148 × 10¹⁸ kg if one accounts for the whole atmosphere and an average value for the water vapour content (Trenberth and Smith 2005).

We will also need to use the heat capacity of the atmosphere. As a first approach, we will consider that the relevant heat capacity to be used is at constant pressure (C_p) and not at constant volume, as we are performing an enthalpy balance. We may also argue that if we consider the global heating of the atmosphere since the atmosphere is not held by rigid boundaries, it is unlikely that the total volume of the atmosphere will remain constant; thus, should the atmosphere change temperature, its volume should also change, expanding if it is heated. In this case, part of the heat that is supplied to the atmosphere will be spent on work done against gravity, which can be taken as constant, implying that isobaric heat capacity can be used as a good approximation. Since the atmosphere is very heterogeneous and the value of C_p changes with both pressure and temperature, we will consider only an average value at ambient conditions. As, under these conditions, air behaves mostly as an ideal gas, for which the heat capacity is not expected to change significantly with temperature, we can use the average value of 1.006 kJ/kg/K (Engineering ToolBox 2004), for 18 ^oC and 1 bar.

Under this set of assumptions, the temperature increase of the atmosphere would be 0.117 K/year in 2019. Although this value is relatively low, if no changes in the energy received vs. energy lost to the surroundings balance occurred, and at a constant energy production level, this would imply a temperature increase in the atmosphere of more than 1 K per decade and 10 K in a century, which is actually significantly more than what is currently expected as the global warming scenario. This result implies that the heat released into the atmosphere, by our energy production/consumption system, is more than enough to justify the observed warming, even if no greenhouse effect is considered.

We must note that this would be a “worst case” scenario (if we exclude any greenhouse effect) as all the thermal energy that is generated was considered to be absorbed by the atmosphere. However, it is likely that part of the energy released will be absorbed by some endothermic processes, such as increased water evaporation and/or ice melting or even the raise in temperature of water bodies and of the Earth’s crust itself. Additionally, as global temperature increases, there may also be an increase in energy that is radiated out of the Earth. On the other hand, if any greenhouse effect is added, this would reinforce the temperature increase.

To further analyse this hypothesis, we looked at the time evolution of energy production from 1971 to 2019 (International Energy Agency 2018; International Energy Agency 2019; International Energy Agency 2020; International Energy Agency 2021) and the temperature anomalies in the global land-ocean temperature index that have been reported up to 2021 (NASA 2022a).

The time-series evolution of these two parameters is represented in Fig. 1.

As it can be seen the two curves follow exactly the same trend, which implies that there may be a correlation between temperature increase and energy production and reinforces the idea that global warming is associated with the energy production system. In fact, we can see that there is a strong correlation between the temperature anomaly and the rate of energy production (Fig. 2).

This is hardly unexpected, and this high correlation may be direct, i.e., the temperature anomaly is caused by the energy production itself, or indirect, such as a relation with CO₂ emissions, which is the current view associated with global warming. The current view linking global warming to the CO₂ (and other greenhouse gases) concentration in the atmosphere (Archer 2012) is, in our opinion, limiting but understandable as most of the energy is produced concomitantly with CO₂ emissions and there is a direct linear relationship between the energy production and the CO₂ emissions, as it can be seen in Fig. 3. In fact, a correlation would also be observed if the temperature anomaly is plotted against the CO₂ emissions.

However, based on the results previously presented, we will inspect the possibility of the increase in temperature being directly linked to the energy that is generated and as discussed above, that is ultimately released as thermal energy to the environment, and not just to the emissions of CO₂.

To compute the expected temperature anomaly induced by the heat released by the generation of energy we assumed, as above, a scenario where there is no imbalance between the energy received from the Earth’s surroundings and the energy sent back to the surroundings (quasi-adiabatic approach). This is a limit case where we consider that all the heat that is released to the atmosphere by the energy production system is accumulated in the atmosphere, an approximation that we will discuss further on. In this way we can compute the cumulative anomaly using the following approach:

$${T}_{year i}={T}_{1970} + \sum _{all \text{y}\text{e}\text{a}\text{r}\text{s}}\frac{{Energy produced}_{year i}}{{M}_{atmosphere}{C}_{p}}$$

Figure 4 – Comparison of the time evolution of the measured (NASA 2022a) and computed temperature anomalies assuming that all the energy is released into the atmosphere (see text).

As it can be seen from this data the temperature anomaly computed using a quasi-adiabatic approach is much higher than the actual anomaly that is observed according to the GISS data; the quasi-adiabatic approach predicts a temperature increase of around 3.9 K in relation to 1971. This reinforces the idea that just considering the energy released into the atmosphere is more than enough to justify the observed warming, but it also indicates that, as expected, the adiabatic approach is not valid in relation to the atmosphere on its one, and that it is likely that part of the energy that is released into the atmosphere is exchanged, for example with the rivers, oceans, ice caps or even with the land masses; In fact, as already discussed, part of the thermal energy released from the energy system is directly released into rivers (Raptis et al. 2016). Additionally, as the temperature of the Earth increases its own radiation will increase and part of the energy may be lost to outer space by the usual radiative process. The main aspect to emphasise here, however, is that the amount of energy released is actually more than enough to justify the observed increase in the average temperature of the Earth.

In the following, we will consider that only a limited fraction of the energy released into the environment is used to heat the atmosphere. The actual temperature anomaly can be fully explained if we consider that only around 24% of the total energy produced is actually consumed by the warming of the atmosphere, and the remainder is exchanged out of the atmosphere, by any of the processes considered above (water warming, water evaporation, ice melting, soil heating, and loss to space). Figure 5 shows that an almost perfect description of the GISS anomalies in the last 49 years can be obtained.

One of the possible heat sinks that can absorb part of this energy is the reduction of the ice sheets. In fact, according to the NASA Global Climate website, the reduction in the ice sheets is currently estimated at 427 Gt/year (NASA 2022b). The melting of this amount of ice in one year corresponds to a consumption of 142 EJ/year (considering a fusion enthalpy of 333,9 kJ/kg), a value which, if compared to the heat released in 2019, corresponds to around 23% of the total heat released, which still leaves a large amount of energy unaccounted for. Again, we can conclude that the amount of energy released by the energy production system is more than enough to justify the observed temperature anomaly, even when taking into account other effects such as the melting of ice caps.

As mentioned above, most of the energy balances made to discuss the temperature evolution of the atmosphere are based on global energy balances and assume that the temperature increase is solely due to an energy imbalance, where the Earth receives more energy than it radiates back into space, and this is the major assumption in many models, for example by the daisyworld models (Paiva et al. 2021).

These models actually assume, albeit implicitly, that the effect of heat generation due to human activity at the surface of the planet is negligible. However, from the results shown above, the amount of heat that is released at Earth’s surface by the energy production and consumption system seems to be relevant to the change of temperature of the atmosphere and can account not only for all the temperature anomaly that is observed but also for the increase in glacier melting, for example.

The apparent correlation between the temperature anomaly and CO₂ emissions that serves as the basis of much of the current discussion on global warming is justifiable since these closely correlate with energy production values as most of the energy production emits CO₂.

From our calculations, the increase in atmospheric temperature may be caused by the conversion of energy that is stored in specific forms, like chemical or nuclear energy, to other forms of energy to be used in current society and ultimately converted into thermal energy that will increase the temperature of the atmosphere even if no other energy exchanges occurred between the Earth system and its surroundings, much as what happens inside an adiabatic chemical reactor.

It can be argued that the amount of energy that we release to the surface by energy production will not be only absorbed by the atmosphere. In fact, part of the energy that is released might be sent directly into water bodies, through the cooling systems of power plants, for example, if they return hot water to the environment. Some energy can also be exchanged, by different mechanisms, including conduction, between the atmosphere and the oceans and lakes or the solid surface itself. Another relevant mechanism is the fact that increasing the temperature of the atmosphere will also increase its energy transfer to the surroundings, oceans, solid surfaces, and outer space. All these effects would reduce the final increase of temperature of the atmosphere as discussed above since an enthalpy balance to the atmosphere indicates that only around 23% of the energy produced seems to be accumulated in the atmosphere. This is also consistent with accelerated glacier melting, water evaporation and ocean warming.

The heat content increases due to the energy production/consumption system, from the calculation above, amounts to 14.7 × 10²¹ J from 1971 to 2010, which compares well to published values (Hansen 2011) and corresponds to a very significant contribution to global heat content increase. The energy released by the energy production system from 1971 to 2019 is already at 20 × 10²¹ J (or 20 ZJ).

In our opinion, there is an additional factor that points to the possibility of the warming effect being linked to energy production and usage. From data (not shown) from the NASA Global Climate website (NASA 2022b) it can be seen that the CO₂ concentration in the atmosphere is more or less uniform throughout the Earth’s surface and, thus, should have a uniform greenhouse effect; however, from the data in the same website, it is clear that the northern hemisphere has a much higher temperature anomaly than the southern one. This, however, is understandable if we consider that most of the energy production and consumption occurs actually in the northern hemisphere.

It should also be noted that this is not the only addition of thermal energy to the environment and other sources must be considered as well as, for example, forest fires or even wars. Forest fires consume a significant area of wood, estimated at around 3.3 to 4.3 km² each year (Verón 2012); the same report estimates that the amount of radiative energy released is about 1 EJ/year, also releasing around 1 Gt of CO₂/year.

The main conclusion that can be drawn from the results presented is that it seems very likely that the heat released in the energy generation and consumption process has a very relevant contribution to this effect and may even be one of the main effects. This results directly from the enthalpy balance to the atmosphere that shows that the energy produced can have a very profound effect on the atmospheric temperature.

This introduces a different view on the phenomenon of global warming as it relates the warming directly to the generation of energy and not just to the emission of greenhouse gases, i.e., directly to the energy emissions and not only to material emissions. In fact, it does not change the urgency of the problem and the fact that global warming is an anthropogenic phenomenon, but it does change the way it should be approached.

If a significant part of the warming is due to the energy that is directly released, the focus for solving this problem should be set on energy efficiency and not, or at least not only, just to the reduction of greenhouse gases as a number of the solutions that are proposed for decarbonisation, for example, associated with carbon capture, actually reduce energy efficiency (Bisinella et al. 2021) and, thus, produce more waste heat that will contribute to the warming. A more detailed analysis of the contribution of the different effects is required.

As further work, the relative importance of the different types of effects that can be related to the increase in the temperature of the atmosphere must be assessed so that a deeper understanding of the mechanisms for global warming can be obtained. The contribution of the heat released by the energy production/consumption system should be included as an anthropogenic forcing effect in the global climate models.

Acknowledgements

The authors would like to thank FCT for financial support through CERENA (project UID/ECI/04028/2020). The authors would also like to acknowledge Prof. Clemente Pedro Nunes (IST-UL, Lisboa), Prof. Edgar Fernandes (IST-UL, Lisboa), and Prof. Jacques C. Védrine (Université Pierre et Marie Currie, Paris) for useful discussions.

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Heating Up the Planet – A Fresh Hot Look at Global Warming

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Abstract

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1. Introduction

2. Preliminary Calculations

3. Time Evolution

4. Discussion

5. Conclusions

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Acknowledgements

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