Let’s put this question into context. It relates to an argument sometimes made by people who reject the idea of human-caused climate change (also called Anthropogenic Global Warming or AGW). It’s an argument used to assert that the “greenhouse effect” can’t possibly be real.
The atmospheric greenhouse effect is a phenomenon in which certain gases absorb and radiate infrared radiation, slowing the rate at which heat escapes the Earth; in the context of the Earth being heated by sunlight, this slowing of heat escaping leads to a rise in temperatures near the surface of the Earth.
(Note that the term “greenhouse” in the name of the effect is a metaphor, not an indication that anyone believes greenhouses and the atmospheric greenhouse effect function in precisely the same way. In both cases, the rate at which heat from the sun is lost is slowed, and this increases temperatures. But, the mechanism whereby heat loss is slowed is different for an actual greenhouse vs. in the greenhouse effect.)
Sometimes people assert that this “greenhouse effect” can’t be true, because they believe the model that predicts this effect has heat flowing from a cooler place (in the atmosphere), to a warmer place (the Earth’s surface), thereby violating the Second Law of Thermodynamics.
This assertion is false.
Various sources of confusion seem to be present:
- It’s important to distinguish heat flow from energy flow. Energy always flows in both directions, from hot to cold and from cold to hot. Heat flow is the net flow of energy. The Second Law of Thermodynamics allows energy to flow from cold to hot, as long as the amount of energy flowing from hot to cold is larger.
- People sometimes rely on informal paraphrasing of the Second Law of Thermodynamics, and such informal re-phrasing can lead to assertions that do not actually follow from the Second Law.
- People sometimes fail to distinguish between the behavior of systems with and without an ongoing flow of energy into them. Intuitions that are helpful in thinking about one type of system can get in the way when thinking about a different type of system.
- People sometimes have strong feelings about what “should” be the right answer, and this can create cognitive distortions that make it harder to understand logic and information that doesn’t seem to lead towards the “right” outcome.
As a physicist, it is very clear to me that the greenhouse effect is a real effect which influences the temperatures of planets. It’s entirely compatible with the Second Law of Thermodynamics.
In what follows, I unpack these ideas in a lot more detail.
Table of Contents
- What is the Greenhouse Effect?
- Experimental verification
- Is heat flowing “the wrong way,” violating the Second Law of Thermodynamics?
- Consistency with heat-flow formulation of the Second Law
- Invalid paraphrasing of the Second Law
- Why intuitions about temperature and heat get confused
- Relation to greenhouse effect
- Cognitive barriers to understanding
- Bonus example: steady-state temperatures
What is the Greenhouse Effect?
Let’s talk about what the atmospheric greenhouse effect is. Below is a diagram showing flows of electromagnetic radiation that affect the temperature of the Earth. This diagram is oversimplified. The models that climate scientists use to predict climate changes are unimaginably more complicated. However, this simple model includes all the elements necessary to explain the greenhouse effect conceptually, and to address the question.
Solar radiation shines on the Earth. The light from the Sun is mostly visible light, although there is also some ultraviolet and infrared radiation. The atmosphere is largely transparent to visible light, and most of the radiation reaches the ground and gets absorbed. We’ll call the rate at which sunlight is absorbed into the Earth’s surface S. This can be specified in units of watts/m².
The surface of the Earth emits thermal radiation, which is mostly in the infrared (IR) part of the electromagnetic spectrum. We’ll call the rate at which the Earth emits infrared radiation R (watts/m²).
Most of the emitted infrared radiation passes out of the atmosphere, and is lost into space. However, certain gases, which are referred to as “greenhouse gasses” (GHG), are able to absorb (and radiate) infrared light. So, some of the infrared radiation emitted by the Earth gets absorbed by these greenhouse gases. This absorbed infrared light is converted to heat.
Greenhouse gasses emit infrared radiation, in all directions. Some of this radiation is lost into space. And, some of this radiation reaches the surface of the Earth and is absorbed. We’ll call the rate at which infrared radiation emitted by greenhouse gasses is absorbed into the Earth Ge (watts/m²).
The surface of the Earth will be at some temperature, Te, specified in Kelvin (so that Te indicates degrees above absolute zero). For purposes of illustration, we’ll assume the surface temperature is the same everywhere. The temperature affects the rate at which the Earth emits thermal radiation. According to the Stefan-Boltzman Law, the power radiated (by the Earth’s surface) per unit area, R, will be given by 𝑅=𝝐𝜎(𝑇𝑒)⁴R=𝝐𝜎(Te)⁴, where 𝜎 is the Stefan-Boltzman constant, and the emissivity 𝝐 is a number between zero and one which reflects the characteristics of the surface.
Now that we’ve established all this, how can we predict the temperature, Te?
The key insight that allows us to determine the Earth’s temperature is this: the net rate of energy flow to and from the Earth’s surface must be zero, on average.
How do we know this is true? If more energy is absorbed than is radiated, then the Earth will heat up. As the temperature rises, more heat will be radiated, and eventually absorption and radiation will balance. Or if less energy is absorbed than is radiated, then the Earth will cool down. As the temperature drops, less heat will be radiated, and eventually the absorption and radiation will balance. It’s a self-correcting system. The temperature adjusts itself until absorption and radiation are balanced.
Now, we need to do some math. By the standards of a physicist, the math is not very hard. But, if you don’t like math, you can just skip ahead to the result.
Because we know the energy flows balance, we know 𝑆+𝐺𝑒=𝑅S+Ge=R, i.e., the energy absorbed by the Earth’s surface equals the energy radiated by the surface (on average). But, recall that the energy radiated by the Earth’s surface is 𝑅=𝝐𝜎(𝑇𝑒)⁴R=𝝐𝜎(Te)⁴. Solving for Te, we find that 𝑇𝑒=(𝑅/(𝝐𝜎))¼Te=(R/(𝝐𝜎))¼, or
𝑇𝑒=((𝑆+𝐺𝑒)/(𝝐𝜎))¼Te=((S+Ge)/(𝝐𝜎))¼ [Equation 1].
Some people may find this equation easier to make sense of if we reformulate it. Suppose that the power of greenhouse gas radiation absorbed by the Earth, Ge, is much smaller than the solar power, S. Then, we could use a Taylor series expansionto write as an approximation
𝑇𝑒≈𝑇0+𝑄×𝐺𝑒Te≈T0+Q×Ge [Equation 2]
(I offer Equation 2 because it’s simpler to understand than Equation 1. However, on Earth, if you average over the globe and over the day, the power delivered to the Earth’s surface by back-radiation, Ge, is actually measured to be over twice the average power of solar radiation, S, absorbed by the surface!)
Whether we look at Equation 1 or at Equation 2, the result is the same: if the greenhouse gas “back-radiation” energy flow, Ge, gets larger, then the Earth’s temperature, Te, increases.
If more greenhouse gases are present in the atmosphere, the rate of greenhouse gas back-radiation gets larger, and this increases the Earth’s temperature.
This is what we call the “greenhouse effect.”
In words, the way it works is as follows. For the Earth to have a stable temperature, the rates of energy absorbed and emitted by the Earth’s surface need to balance. If greenhouse gases are present in the atmosphere, they increase the total rate of energy absorbed by the Earth’s surface. To balance this, the Earth’s temperature increases, causing the Earth’s surface to emit more thermal radiation, thereby restoring balance.
The basic principles of the greenhouse effect are easy to demonstrate experimentally in a laboratory. For example, one can experimentally demonstrate that, in the presence of a heating lamp, CO₂ can contribute to raising the temperature of an underlying surface. Demonstrating this is simple enough that it is sometimes done by college students as a lab experiment.
Such experiments don’t address the full complexity of what happens in the Earth’s atmosphere. But, they do disprove assertions that the greenhouse effect violates basic physics and can’t possibly happen.
Is the greenhouse effect counter-intuitive?
Some people will look at the analysis and say something like, “Wait a minute, the energy that is coming to the Earth from greenhouse gases started out at the Earth’s surface—it’s not ‘new’ energy, so how can that increase the temperature of the Earth’s surface? It doesn’t make sense.”
It doesn’t matter if the energy was previously at the Earth’s surface. All that matters is that it’s coming back to the Earth’s surface.
It’s much like the way that a “space blanket” works. A “space blanket” is a reflective film that we can wrap around us to support survival in cold weather. It reflects our body’s warmth, thereby helping to keep us warmer than we would be without it. It doesn’t matter that the energy started out in our body. Having that energy reflected back to us still helps us keep warm.
You might still say, “The greenhouse effect doesn’t intuitively make sense to me. It can’t be true.”
To which, one might reply “Get over it. Intuition does not determine reality!”
The history of science is full of examples of scientists discovering, again and again and again, that the world does not work the way we naively expect it to.
Consider some theories at the heart of modern physics, as well as key applications of physics:
- quantum mechanics
- nuclear fission and fusion
- orbital mechanics
- semiconductor electronics
- global positioning systems (which require time corrections based on both special and general relativity in order to provide accurate location information).
All of these include aspects that work differently than people “intuitively” would have expected.
Intuition can be useful. But, it’s not a reliable guide to scientific truth. Our intuition needs to be checked with careful mathematical analysis and experiments. Both of these confirm that greenhouse gases raise the temperatures of planets.
Is heat flowing “the wrong way,” violating the Second Law of Thermodynamics?
The Second Law of Thermodynamics is often expressed as something like “heat flows naturally from an object at a higher temperature to an object at a lower temperature, and heat doesn’t flow in the opposite direction”—plus some pesky qualifiers.
What do I mean by “pesky qualifiers”? Well, there need to be qualifiers for things like refrigerators to be possible. Those qualifiers are “pesky” because they can be tricky to express simply and accurately.
One statement of the law is “Heat flows from a hot object to a cold object unaided but it cannot flow from a cold object to a hotter object without the expenditure of mechanical energy.” Unfortunately, this way of expressing the qualifiers is not strictly correct. This is demonstrated by the existence of Peltier thermoelectric coolers that move heat from cold to hot electrically, without any “expenditure of mechanical energy.”
Fortunately, we can make progress on this discussion without getting the details of those “pesky qualifiers” sorted out.
Some people argue that the Second Law means that the greenhouse effect can’t happen:
“Something cooler (greenhouse gases in the atmosphere) can’t raise the temperature of something warmer (the Earth’s surface). Therefore the greenhouse effect can’t happen!”
Let’s examine this claim.
Consistency with heat-flow formulation of the Second Law
Does the greenhouse effect involve heat improperly flowing from the cool atmosphere to the warmer surface of the Earth?
It’s important to look at what it means for heat to flow from one thing to another.
As Wikipedia notes, the flow of heat “means ‘net transfer of energy as heat’, and does not refer to contributory transfers one way and the other.” It is always the case that energy flows in both directions. Heat flow is the difference, when one subtracts the energy flow in one direction from the energy flow in the other direction.
What the Second Law of Thermodynamics requires is that the flow of energy from hot to cold is larger than the flow of energy from cold to hot.
Does the greenhouse effect model, described above, violate this principle?
No, the power flux of infrared radiation going from the ground to the greenhouse gases, Rg, is larger than the power flux of infrared radiation from the greenhouse gases to the ground, Ge. So, overall, heat (the net difference) is flowing from the ground into the atmosphere.
Thus, the greenhouse effect model is entirely consistent with any formulation of the Second Law of Thermodynamics that says “heat flows naturally from an object at a higher temperature to an object at a lower temperature.”
Invalid paraphrasing of the Second Law
“But wait a minute,” says the person who objects to the reality of the greenhouse effect. “You’re still claiming that something cooler (the atmosphere) is raising the temperature of something warmer (the Earth’s surface). That is a violation of the Second Law of Thermodynamics!”
But does it actually follow from the Second Law of Thermodynamics that “something cooler can never raise the temperature of something warmer”? No, it doesn’t.
There is no statement like that which is part of the common formulations of the Second Law of Thermodynamics and its corollaries.
You might intuitively think that this statement about temperatures is equivalent to the prior corollary about heat flow, but it’s not. Temperature and heat flow are different things.
I challenge those who think the greenhouse violates the Second Law to find a serious physics text that says “something cooler can never raise the temperature of something warmer” without there being a number of (explicit or implicit) qualifiers that leave a relevant “out” from this rule. Without qualifiers and precise definitions of terms, the statement isn’t true.
Why intuitions about temperature and heat get confused
How heat and temperature relate to one another depends, in some ways, on the type of system one is considering.
One way of looking at is this: it’s simple to understand what happens in an isolated system with only two objects in it (and people tend to base their intuitions about heat and temperature on this situation). Yet, things get more complicated, when there are three or more objects in a system, or heat flows into and out of the system.
So, those who base their intuition on considering a system with only two objects might say “a cooler object can never raise the temperature of a warmer object.” Yet, this is not true in general.
A more generally accurate statement would be “a cooler object can never, by itself, raise the temperature of a warmer object.”
That qualifier, “by itself,” is critical. Because, when we look at more complicated systems, we often find that a cooler object—in combination with a separate heat source or a heat sink or other influences—can in fact increase the temperature of a warmer object. It is something that happens through a combination of influences, not something that the cooler object does by itself.
Typically, what happens is that the cooler object effectively slows the rate at which another object cools, thereby allowing a separate heat source to increase the temperature of the object of interest.
In summary, I think people often develop intuition that correctly describes what happens in one type of system, and try to apply that intuition to a different type of system. Unfortunately, that often doesn’t work. Intuitions formed by thinking about the one type of systems are likely to be a poor guide to understanding what happens in another type of system.
I think this point might become clearer if we consider some related examples to help to illustrate the way that different types of systems work differently.
In each example, we’ll consider how the presence of a cooler object C affects the temperature of a warmer object A.
Example 1: System with no energy flows in or out
Consider the illustration below.
There is a perfectly insulated chamber. Inside are two or three objects. Initially, the temperature of object A is the hottest, and the temperature of object C is the coldest.
What will happen?
- Heat will flow between the various objects.
- Eventually, objects A, B and C (if present) will reach the same temperature.
- Because object C is the coldest, object A will become colder (have a lower temperature) in Configuration Y than in Configuration X.
- Object C has a net cooling effect on object A.
Example 2: System with outward heat flow
In this example, the chambers are open on one side to the outside environment. Let’s suppose that the outside air temperature is 0ºC, and that object A starts out much warmer than this. Object’s B and C are assumed to have low heat capacity, and to behave as (imperfect) insulators.
What will happen?
- Heat will flow between the various objects, and out into the environment.
- Eventually, objects A, B and C (if present) will reach a temperature of 0ºC, matching the temperature of the environment.
- Object C acts as an insulator, slowing the flow of heat to the environment. Consequently, at any given time after the experiment starts, the object A will be warmer in configuration Y than it is in configuration X, though the temperature of object A will never be higher than its starting temperature.
- Object C has a net effect of slowing the rate of cooling of object A.
- Object C It has no effect on the final steady-state temperature of object A.
Example 3: System with heat flows both inward and outward
This example is like the previous one, with the addition of an energy source that continuously adds heat to object A.
Let’s provide some specific numbers, to make the example concrete:
- Let’s assume there is a 100 watt electric heater that runs continuously.
- Again, let’s suppose that the outside air temperature is 0ºC.
- In this situation, we will need to know specific information about the insulators. Let’s assume that the opening to the environment has an area of 10 square meters, and that each insulator, B and C, has an insulation R-value of 1 °C⋅m²/W (equivalent to a U.S. R-value of 5.7 °F⋅ft²⋅h/BTU).
Let’s look at the steady-state temperature that develops after the system has come into equilibrium. Note that the initial temperatures of objects A, B and C (if present) have no effect on the final steady-state temperatures.
How can we figure out the steady-state temperature of object A?
In steady-state, the energy coming into object A and the energy leaving object A must be the same. If these energy flows are not the same, object A will either heat up, or cool down, until it has reached a state in which these energy flows are equal.
Thus, if 100 watts is flowing into object A, there must also be 100 watts flowing out of object A, through objects B and C (if present), into the environment.
If we assume the heat flow is uniform over the 10 m² area of the opening, this means a heat flux φ = (100 watts)/(10 m²) = 10 watts/m². Given the definition of insulation R-value, the temperature drop across an insulator is just the heat flux times the R-value. This means that the temperature drop (between inside and outside the chamber) in configuration X (with an R-value of 1 °C⋅m²/W) will be 10°C, while the temperature drop in configuration Y (with an R-value of 2 °C⋅m²/W) will be 20°C. Given that the outside temperature is 0°C, and assuming perfect heat conduction within the chamber, this means that the steady-state temperature of object A will be 10°C in configuration X and 20°C in configuration Y.
- Heat will flow into object A, between the various objects, and out into the environment.
- The initial temperatures of objects A, B and C (if present) are irrelevant to the final, steady-state temperatures.
- In the configuration where object C is absent, the steady-state temperature of object A is 10°C, and in the configuration where object C is present, the temperature of object A is 20°C.
- The net effect of object C being present (in combination with the heater) is to increase the steady-state temperature of object A. This is true even though object C is cooler than object A.
This result doesn’t involve any exotic physics. The math is simple enough that it could be done by any heating contractor. And, if you don’t believe the math, it would be simple to do an experiment to check the prediction. The physics here is beyond any doubt.
Some people might want to say this result claims “a colder object, C, is raising the temperature of a hotter object, A”—and see this result as suspect. But, that is a misleading and confusing way of talking about what is happening in this example.
It would be clearer to say:
- object C is slowing the rate at which heat leaves object A;
- there is no net heat flow from object C to object A;
- yet, in a context in which heat is continuously flowing into object A, any slowing of heat leaving leads to the temperature of object A increasing.
People who focus on thinking about systems like those in Examples 1 and 2 may find the result for Example 3 does not match their intuition.
Understanding Example 3 requires a different mode of thought than what suffices for Examples 1 and 2. One needs to think about balancing energy to achieve steady-state; this approach was not needed in the prior examples. If one is unable to shift to a different mode of thinking, it is understandable that the outcome in Example 3 might seem baffling.
If Example 3 doesn’t make sense, this is not an indication that mainstream physics is wrong. It’s an indication that it might be time for you to examine your thinking, and shift to a new way of thinking that better matches reality for this type of system.
For what it’s worth, here is another resource that addresses this issue of a cooler object having the effect of a leading to a higher temperature for a warmer object: http://www.drroyspencer.com/2010/07/yes-virginia-cooler-objects-can-make-warmer-objects-even-warmer-still/
Relation to greenhouse effect
Although the physics in the greenhouse effect is a little more complicated than in the case of a heated chamber, it involves the same category of system as is presented in Example 3. Both cases involve a system in which energy is flowing both into and out of the system.
The Second Law of Thermodynamics is consistent with both Example 3 and the earlier model illustrating the greenhouse effect.
Cognitive barriers to understanding
Those who reject the mainstream science about global climate change often seem outraged by what they believe would be the political implications if human-caused global climate change (AGW) were a reality. There’s also often a level of contempt and scorn present that suggests the presence of intense emotions. These understandable worries and emotions are powerful fuel for “motivated reasoning.”
When “motivated reasoning” is active, a strong preference is given to any information that supports the desired conclusion, and information that counters the desired conclusion is not fairly considered. It’s not a conscious process. There are cognitive blocks that simply make it almost impossible to take in certain information or understand certain arguments. There may be an inability or an aversion to going through details, step by step, to unravel the truth.
If you’re feeling strong emotions about this subject, I hope you’ll consider slowing down and going through the logic without preconceptions.
There are many things about the world that I very much wish worked differently than they do. Personally, I don’t want it to be true that humans are causing dangerous global climate change. Yet, I want to discover how the world actually works, regardless of my preferences.
* * *
Bonus example: steady-state temperatures
[After I wrote my original answer, it occurred to me that the following example might be helpful to some people. So, in case it is helpful to you…]
Let’s look at an example with two variants. In both situations, there is a “hot” object (at a temperature of 200 Kelvins) and a “cold” object (at a temperature of 100 Kelvins). These hot and cold objects are assumed to have fixed temperatures.
We place another object, A, in between the hot and cold objects, in a vacuum, and ask the question “In steady-state, what is the temperature of object A?” The answer is depicted in the following diagram.
The temperature of object A will be 171K. How does one come to this conclusion?
Each object radiates electromagnetic radiation according to the Stefan-Bolzmann law, so that R = 𝜎 (T)⁴. (Objects are assumed to be ideal “black body” radiators with emissivity 𝝐 = 1.)
This implies that the power (radiant flux) emitted by the hot and cold objects, respectively, is Rh = 221 and Rc = 14. (For all radiation and heat flows, I’m using units of 10−1610−16 Watts/m².)
What about object A? Its temperature will adjust until the radiant flux emitted exactly balances the radiant flux absorbed. One simply adjusts the temperature Ta until this balance is achieved. (One can solve for Ta analytically or numerically. I obtained all the results in this section analytically, but am not certain if including the math would be helpful.)
At a temperature Ta = 171K, the amount of power A radiates in each direction is Ra = 117. The total power absorbed by A is 235 and the total power emitted is also 235. (The numbers seem to be “off by 1” because I am computing the numbers precisely, but only reporting round numbers.)
“Heat flow” is the difference between the radiant flux in the two directions. When we compute the heat flow, we discover that the heat flowing from the hot object to object A is Qha = 104, and the heat flowing from object A to the cold object is also Qac = 104. As expected, the heat flowing into and out of A is identical. That’s why the temperature of A is not changing.
Now, let’s change things by adding another object, B, into the situation.
Again, the hot and cold objects have fixed temperatures, and the temperatures of objects A and B are unknown until we solve for them. The diagram below shows the result.
In this situation, it turns out that, in steady-state, the temperatures of the objects are Ta = 182K and Tb = 157K.
(Again, we assume radiated power is given by R = 𝜎 (T)⁴, and we solve by adjusting the temperatures of A and B until the radiant flux emitted by each of the middle objects matches the radiant flux absorbed by that object. A emits and absorbs 304 (×10−16×10−16 Watts/m²), while B emits and absorbs 166. The amount of heat flowing between each pair of objects is 69. It all balances, as it must in steady-state.)
In summary, if there is one object, A, between the hot and cold fixed-temperature objects, A will have a temperature of 171K. If there are two objects, A and B, between the hot and cold fixed-temperature objects, A will have a temperature of 182K and B will have a temperature of 157K.
Object A is cooler in Configuration L (with no other object present), and warmer in Configuration M (with an additional object placed between it and the cold sink).
In the “real world”, this is a bit similar to what happens if one tries to cook food over a fire. Covering the food with aluminum foil allows the fire to raise the food to a higher temperature. (Of course, in this example, some of what happens is related to convection and not just thermal radiation. But, even in a vacuum, adding foil would allow a heat source to raise the food to a higher temperature.)
This result ought to make sense.
Yet, some people will think about this in a way that confuses them and makes them think “this is impossible.”
They’ll say something like
“Object B is cooler than object A. A cooler object cannot increase the temperature of a warmer object. So, it can’t be true that adding object B increases the temperature of object A!”
The problem with this logic is that the statement “A cooler object cannot increase the temperature of a warmer object” is not a universal truth (unlike the statement “Heat does not naturally flow from a cooler object to a warmer object”).
People who insist that “A cooler object cannot increase the temperature of a warmer object” are likely thinking of a situation like the one shown below.
If objects A and B are the only objects present, and A is warmer than B, then in this situation it is true that the cooler object (B) cannot increase the temperature of the warmer object (A).
But, it’s simply not a universal truth that “The presence of a cooler object cannot increase the temperature of a warmer object.” This is demonstrated by comparing configurations L and M above.
What is a universal truth is that “in the absence of any heat-pumping mechanism, heat never flows from cold to hot.” All three configurations, L, M and P, honor this principle.
I think part of the problem is that the phrasing about a “cooler object increasing the temperature of a warmer object” is sloppy: it fails to distinguish simple situations (in which only one object exists to influence another) and complex situations (in which multiple objects exists and the outcome is a combined result of all the objects that are present).
In configuration M, it’s imprecise and misleading to say that “cooler object B raises the temperature of warmer object A.” It more precise and clearer to say, “the introduction of object B slows down the rate at which heat departs object A, thereby allowing the ‘hot’ object to heat A to a higher temperature.”
It’s not that the cooler object by itself increases the temperature of a warmer object. The rise in temperature is a combined effect of all the objects (and energy flows) present in the system.
People get into trouble, and arrive at incorrect conclusions, if they look at a situation like Configuration P and explain to themselves what happens in a way that does not correctly generalize to other situations (like Configurations L and M).
Configurations L and M offer an example of a situation where introducing another object can lead to another object’s temperature increasing.
The atmospheric greenhouse effect differs in some respect from what happens in Configurations L and M.
Yet, it’s similar in the sense that both analyzing both situations yields answers that are consistent with any correct formulation of the Second Law of Thermodynamics (e.g., “heat flows from hot to cold”), but which violate some naive, false rephrasings of the Second Law (e.g., “a cooler object can’t raise the temperature of a warmer object”).