Climate Change, the Greenhouse Effect and Heat Engines – Laws of Thermodynamics (Senior 4 Physics) | Ganzaa

Laws of Thermodynamics

Lessons

Senior 4 · Physics

Laws of Thermodynamics

5 lessons

Lesson 5 of 5

Climate Change, the Greenhouse Effect and Heat Engines

25 min

A line that keeps climbing

Since 1958, an observatory high on the Mauna Loa volcano in Hawaii has measured the carbon dioxide in the air almost every day. In 1960 the yearly average was 316.9 parts per million (ppm); in 2025 it was 427.4 ppm (NOAA). Before the Industrial Revolution, when people began burning coal, oil and gas in heat engines on a large scale, it was 280 ppm or less (NOAA Climate.gov, 2025). Almost every heat engine you have met in this unit, from a lorry's diesel to a peat-fired power station, burns fuel and adds carbon dioxide to the air. In this final lesson you use the physics of heat and radiation to explain how that gas warms the planet, and why engines matter to the climate.

Figure 5.1: The annual mean carbon dioxide concentration at Mauna Loa, every fifth year from 1960 to 2025. Data: NOAA Global Monitoring Laboratory (1958–1974 data from C. D. Keeling, Scripps Institution of Oceanography); chart drawn by Ganzaa.

A planet in energy balance

Every body radiates electromagnetic energy, and the hotter it is, the more it radiates. For an ideal radiator (a black body) the power radiated per square metre of surface is given by the Stefan–Boltzmann law,

\frac{P}{A} = \sigma T^{4}, \qquad \sigma = 5.67 \times 10^{-8}\,\mathrm{W\,m^{-2}\,K^{-4}}

where $T$ is in kelvin. The Earth gains energy from sunlight and loses it by radiating infrared into space. Averaged over the whole globe, day and night, and after about 29% of the sunlight is reflected straight back to space, the Earth system absorbs about $240\,\mathrm{W\,m^{-2}}$ (NOAA). Its temperature settles where it radiates exactly as much as it absorbs. If the Earth had no atmosphere that absorbs infrared,

\sigma T^{4} = 240\,\mathrm{W\,m^{-2}} \quad\Rightarrow\quad T = \left(\frac{240}{5.67 \times 10^{-8}}\right)^{\frac{1}{4}} = 255\,\mathrm{K} \approx -18\,^\circ\mathrm{C}

NASA gives this "black-body temperature" of the Earth as 254 K, but the measured average surface temperature is 288 K, about 15 °C (NASA). The 33 K difference is the natural greenhouse effect, without which the oceans would freeze.

How greenhouse gases work

Sunlight is mostly visible light, which passes through the air almost unhindered and is absorbed by the ground and the oceans. The warm surface radiates in the infrared, at much longer wavelengths. Molecules of water vapour, carbon dioxide, methane and nitrous oxide absorb infrared at these wavelengths and re-emit it in all directions, some of it back down to the surface (Figure 5.2). The surface is therefore warmed both by the Sun and by the atmosphere above it, and it settles at a higher temperature than it would without these greenhouse gases. The main gases of the air, nitrogen and oxygen, hardly absorb infrared at all.

Adding more carbon dioxide makes the atmosphere absorb more of the outgoing infrared, so for a while less energy escapes than arrives. The planet keeps gaining energy, mainly in the oceans, and warms until it radiates enough to restore the balance. This is the enhanced greenhouse effect behind present climate change. NOAA estimates that the long-lived greenhouse gases added since before the Industrial Revolution retained an extra $3.54\,\mathrm{W\,m^{-2}}$ of heat in 2024, about 1.5% more than the $240\,\mathrm{W\,m^{-2}}$ the Earth absorbs from the Sun, and that carbon dioxide caused about two-thirds of it.

Figure 5.2: Earth's average energy balance (simplified). Greenhouse gases absorb infrared from the surface and send some of it back down.

Definition

The greenhouse effect is the warming of a planet's surface because gases in its atmosphere absorb the infrared radiation emitted by the surface and re-emit part of it back downwards. Greenhouse gases are gases that absorb infrared strongly: water vapour, carbon dioxide ( $\mathrm{CO_2}$ ), methane ( $\mathrm{CH_4}$ ) and nitrous oxide ( $\mathrm{N_2O}$ ). The enhanced greenhouse effect is the extra warming caused by the increase in these gases from human activity. Example: the natural greenhouse effect raises the Earth's average surface temperature from about 255 K to 288 K.

Worked example 1: how fast is carbon dioxide rising?

Use the Mauna Loa data: 316.91 ppm (1960), 325.68 ppm (1970), 401.01 ppm (2015), 427.35 ppm (2025). Find the average yearly rise in the 1960s and over 2015 to 2025.

\text{1960s: } \frac{325.68 - 316.91}{10} = 0.88\,\mathrm{ppm\ per\ year}, \qquad \text{2015 to 2025: } \frac{427.35 - 401.01}{10} = 2.6\,\mathrm{ppm\ per\ year}

The concentration is not just rising, it is rising three times faster than in the 1960s, because the world burns far more fuel each year.

Heat engines and the climate

A heat engine affects the climate in two ways. First, by the second law, it must reject heat to its surroundings. Second, if it burns a fuel containing carbon, it releases carbon dioxide. Which matters more? In 2025 the world used about 178 000 TWh of primary energy, about $6.4 \times 10^{20}\,\mathrm{J}$ (Our World in Data). Spread over the year and over the Earth's surface of $5.1 \times 10^{14}\,\mathrm{m^{2}}$ , all of it, ending as heat, comes to only about $0.04\,\mathrm{W\,m^{-2}}$ . The extra heat retained by greenhouse gases, $3.54\,\mathrm{W\,m^{-2}}$ , is about ninety times larger. The engines' waste heat warms cities locally, but globally it is their carbon dioxide that counts, and much of it stays in the air for centuries.

That is why the answers lie in this unit and in Unit 6: more efficient engines (more work for the same fuel), electricity from sources that burn no carbon (hydro, solar, wind, geothermal), heat pumps instead of fuel heating, and less wasteful use of energy. Rwanda has set itself a target in its Nationally Determined Contribution under the Paris Agreement: to cut greenhouse-gas emissions by 38%, about 4.6 million tonnes of carbon dioxide, by 2030, with energy measures making up 34% of the planned reduction, and to become a carbon-neutral economy by 2050 (Ministry of Environment). Rwanda is also exposed to the effects: MINEMA's 2025 report describes frequent climate-related hazards, especially strong winds, lightning and heavy rain (MINEMA, 2025).

Worked example 2: the carbon dioxide from a car

Treat petrol as octane, $\mathrm{C_8H_{18}}$ (molar mass 114 g/mol), of density $0.74\,\mathrm{kg\,L^{-1}}$ . It burns as $2\,\mathrm{C_8H_{18}} + 25\,\mathrm{O_2} \rightarrow 16\,\mathrm{CO_2} + 18\,\mathrm{H_2O}$ . Find the mass of $\mathrm{CO_2}$ released per litre, and per 100 km by a car using 6.0 L per 100 km.

\frac{m_{\mathrm{CO_2}}}{m_{\text{octane}}} = \frac{16 \times 44}{2 \times 114} = 3.09, \qquad \text{per litre: } 0.74 \times 3.09 = 2.3\,\mathrm{kg}

Per 100 km: $6.0 \times 2.28 = 14\,\mathrm{kg}$ of carbon dioxide. A litre of petrol makes more than three times its own mass of $\mathrm{CO_2}$ , because each carbon atom picks up two oxygen atoms from the air.

Worked example 3: waste heat against greenhouse heating

Using the figures above ( $6.4 \times 10^{20}\,\mathrm{J}$ per year, Earth's surface $5.1 \times 10^{14}\,\mathrm{m^{2}}$ , one year $= 3.16 \times 10^{7}\,\mathrm{s}$ ), find the average heating per square metre from all human energy use, and compare it with $3.54\,\mathrm{W\,m^{-2}}$ .

P = \frac{6.4 \times 10^{20}}{3.16 \times 10^{7}} = 2.0 \times 10^{13}\,\mathrm{W}, \qquad \frac{P}{A} = \frac{2.0 \times 10^{13}}{5.1 \times 10^{14}} = 0.040\,\mathrm{W\,m^{-2}}

The ratio is $\frac{3.54}{0.040} \approx 90$ . Even if every engine were 100% efficient, the climate problem would remain unless the carbon dioxide stopped.

Warning

Common mistakes. (1) Saying greenhouse gases "trap sunlight": sunlight passes through; they absorb the infrared emitted by the surface. (2) Thinking the greenhouse effect is entirely bad: without it Earth would average about −18 °C; the problem is the enhanced effect. (3) Confusing the ozone hole with the greenhouse effect: they are different problems. (4) Thinking waste heat from engines is the main cause of global warming: their carbon dioxide matters about ninety times more.

Tip

Balance in, balance out. In equilibrium, energy absorbed = energy radiated: $240\,\mathrm{W\,m^{-2}} = \sigma T^{4}$ gives 255 K. Greenhouse gases do not add energy; they slow its escape, so the surface must warm to restore the balance.

How Do Greenhouse Gases Actually Work? (MinuteEarth). Watch how molecules of carbon dioxide absorb and re-emit infrared radiation from the ground, slowing its escape to space, as shown in Figure 5.2.

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Practice

Using $\sigma T^{4} = 240\,\mathrm{W\,m^{-2}}$ , find the Earth's average temperature if there were no greenhouse effect, and compare it with the measured 288 K.
A surface at 288 K radiates $\sigma T^{4}$ . Find this power per square metre, and explain why it is larger than the 240 W per square metre that leaves the top of the atmosphere.
From the Mauna Loa data, find the average yearly rise in carbon dioxide from 1960 to 2025, and the percentage increase over that period.
A car uses 8.0 L of petrol per 100 km. Using Worked example 2, find the carbon dioxide it releases on a 300 km journey.
A methane-fired power station of efficiency 33% delivers 1.0 GWh of electricity. Using 0.055 kg of $\mathrm{CO_2}$ per MJ of fuel energy (Unit 6), find the heat it rejects and the carbon dioxide it releases.
Rwanda plans to cut emissions by about 4.6 million tonnes of $\mathrm{CO_2}$ by 2030, with energy measures giving 34% of the cut. How many tonnes is that? Name two energy measures from Unit 6 that help.
Explain why carbon dioxide lets sunlight through but absorbs the radiation emitted by the Earth's surface.
A student says: "Engines warm the planet mainly by the heat they give out, so making them more efficient will solve climate change." Evaluate this statement.

Show answersHide answers

$T = \left(\frac{240}{5.67 \times 10^{-8}}\right)^{\frac{1}{4}} = 255\,\mathrm{K}$ ; 33 K colder than the measured 288 K, the warming due to the natural greenhouse effect.
$5.67 \times 10^{-8} \times 288^{4} = 390\,\mathrm{W\,m^{-2}}$ . Much of the surface's infrared is absorbed by greenhouse gases and some is sent back down; the radiation leaving to space comes mostly from the colder upper atmosphere, and in balance equals the 240 W per square metre absorbed.
$\frac{427.35 - 316.91}{65} = 1.7\,\mathrm{ppm}$ per year; $\frac{110.44}{316.91} \times 100\% = 35\%$ .
Fuel used: $8.0 \times 3 = 24\,\mathrm{L}$ ; $\mathrm{CO_2} = 24 \times 2.28 = 55\,\mathrm{kg}$ .
Electricity $= 3.6 \times 10^{12}\,\mathrm{J}$ ; fuel energy $= \frac{3.6 \times 10^{12}}{0.33} = 1.09 \times 10^{13}\,\mathrm{J}$ ; heat rejected $= 7.3 \times 10^{12}\,\mathrm{J}$ ; $\mathrm{CO_2} = 1.09 \times 10^{7}\,\mathrm{MJ} \times 0.055 = 6.0 \times 10^{5}\,\mathrm{kg}$ , about 600 tonnes.
$0.34 \times 4.6 \times 10^{6} = 1.6 \times 10^{6}$ tonnes. Examples: more electricity from hydro and solar instead of peat, methane and diesel; improved cookstoves and efficient lamps and appliances; reducing grid losses.
Molecules absorb radiation only at particular wavelengths, which depend on how their atoms can vibrate. $\mathrm{CO_2}$ absorbs strongly at infrared wavelengths, where the Earth (at about 288 K) radiates most, but hardly at all at the visible wavelengths where most of the Sun's energy (from a surface at about 5800 K) arrives.
The statement is wrong. All the world's energy use, ending as heat, adds only about 0.04 W per square metre on average, while the extra greenhouse gases retain about 3.54 W per square metre (NOAA), about ninety times more. Efficiency helps only because it burns less fuel and so releases less carbon dioxide; the main remedy is to stop releasing carbon dioxide, by switching to sources that burn no carbon and by using less energy.

Quick check

Key points

Stefan–Boltzmann: $\frac{P}{A} = \sigma T^{4}$ . Absorbed sunlight (about $240\,\mathrm{W\,m^{-2}}$ ) balanced by radiation gives 255 K; the real average is 288 K: the natural greenhouse effect.
Greenhouse gases ( $\mathrm{H_2O}$ , $\mathrm{CO_2}$ , $\mathrm{CH_4}$ , $\mathrm{N_2O}$ ) absorb the surface's infrared and re-emit part of it downwards.
$\mathrm{CO_2}$ at Mauna Loa rose from 316.9 ppm (1960) to 427.4 ppm (2025), from 280 ppm or less before industry (NOAA).
Heat engines matter to climate mainly through their $\mathrm{CO_2}$ , not their waste heat; efficiency, carbon-free electricity and saving energy all help. Rwanda's NDC targets a 38% cut (about 4.6 Mt $\mathrm{CO_2}$ ) by 2030.

1A line that keeps climbing

2A planet in energy balance

3How greenhouse gases work

4Heat engines and the climate

A line that keeps climbing

A planet in energy balance

How greenhouse gases work

Heat engines and the climate