For every 1°C of temperature increase in the atmosphere, on the Planet the heat increases by 0.34%.

Author; Rogelio Pérez C

Summary;

In the climate change problem, knowing how much heat on the planet increases for every degree centigrade that the temperature increases in the atmosphere is the main key to understanding the problem known as global warming, for we would know precisely what is the true critical point or "point of no return" that could be catastrophic for the planet. The theory of the greenhouse effect, which is one of the sciences that teaches how the temperature increases on the planet, explains that the increase of certain gases in the atmosphere known as greenhouse gases is the cause of the temperature and the atmospheric heat, according to this, we live almost on the brink of a climate catastrophe due to the increase in these gases.The greenhouse effect theory uses a concept called equilibrium climate sensitivity to explain the temperature changes caused by this effect. And it consists of a hypothetical value given in degrees Celsius to validate its hypothesis, but hypothetical values are assumptions.But the kinetic theory of gases, which is the other theory with which we can explain the temperature and atmospheric heat, shows us mathematically, as soon as the heat on the planet increases, when the temperature rises 1 degree Celsius. Although the concepts of heat and temperature are related to each other, they have different characteristics, because while temperature is the measure of the kinetic movement of atoms or molecules within a system, and it is given in degrees Celsius, heat is the transfer of this energy between atoms or molecules of different systems, and it is given in Joules. With this work I show that the increase in the heat level in the gas molecules that make up the atmosphere is 12.46 joules or 0.34% of the heat, when the temperature of the molecules increases by a degree centigrade.

Introduction

The world is currently implementing many strategies to address the global climate problem, based on the science of greenhouse effect theory, and the best solution today is the reduction of certain gases in the atmosphere, called greenhouse gases, such as CO2,The greenhouse effect theory uses a concept called equilibrium climate sensitivity to explain the temperature changes caused by this effect. And it consists of a hypothetical value given in degrees Celsius to validate its hypothesis, but hypothetical values are assumptions.This work is written to show a new way of understanding the climate on the planet, based on the kinetic theory of gases, so that we can better understand the problem of heat on the planet. According to the greenhouse effect theory, infrared radiation and the gases that absorb this energy are the cause of the increase in atmospheric heat, but according to this research the absorption of infrared radiation by greenhouse gases, it cannot be the cause of the temperature increase in the atmospheric system, because 99.9% of the molecules in this system do not absorb infrared, although all molecules in this atmospheric system emit infrared, which allows to measure their temperature, Since infrared emitted by the earth's surface, which are absorbed and retained by greenhouse gases in the atmospheric system, is the cause of the infrared emitted by the atmosphere, this would nullify the capacity of the gas molecules that make up the atmospheric system to cause its own temperature.

Science teaches that the temperature of any system is given by the measurement of the kinetic energies of the atoms or molecules that compose it, but heat is the kinetic energy that can be transferred by the atoms or molecules of a system, to the atoms or molecules of other systems with less kinetic energy, this work measures the differences in the kinetic energies of the main gas molecules that make up the atmosphere, when they are at 14°C and 15°C, to know the difference in heat, which gas molecules in the atmosphere can transfer to other systems, when their temperature increases by 1 degree Celsius.

Theory statement and definitions

The greenhouse effect theory

The greenhouse effect is a process in which thermal radiation emitted by the planetary surface is absorbed by atmospheric greenhouse gases (GHGs) and radiated in all directions. As part of this radiation is returned to the Earth's surface and lower atmosphere.1

How is the temperature in the greenhouse effect theory explained? 

This uses a concept called climate sensitivity, which is a measure of how the temperature of the climate system responds to a change in the radiative forcing (the difference between the solar light absorbed by Earth and the energy radiated back into space). This shows as the temperature change associated with a doubling of the concentration of carbon dioxide in the atmosphere. 1.1

How is temperature measured based on greenhouse effect theory? 

This measures temperature based on the equilibrium climate sensitivity range. 

What is the equilibrium climate sensitivity range? 

(ECS, is a hypothetical value (assumption or some possible or impossible theory to draw any particular consequence, cause, or reason) of equilibrium global warming to double CO2. And because it is a hypothetical value it may change according to the researcher, but the greatest value used in the models generated in the 1990s, is the hypothetical value of 1.8°C to 5.6°C.1.2

Kinetic of gases theory

The kinetic of gases theory is a physical and chemical theory that explains the macroscopic behavior and properties of gases (the law of ideal gases), based on a statistical description of microscopic molecular processes. The kinetic theory was developed based on studies by physicists such as Daniel Bernoulli in the 18th century, Ludwig Boltzmann and James Clerk Maxwell in the late 19th century.2

Charles law for gases, for any gas, the ratio between temperature and volume is directly proportional, if the quantity of gas and pressure remain constant.

Mathematically we can express it like this:

Where;

V is the volume

T is the absolute temperature (i.e measured in kelvin).

k is the constant of proportionality.3

Heat, q, is thermal energy transferred from a hotter system to a cooler system that are in contact. Temperature is a measure of the average kinetic energy of the atoms or molecules in the system. The zeroth law of thermodynamics says that no heat is transferred between two objects in thermal equilibrium; therefore, they are the same temperature.4

Heat, is thermal energy transferred from a hotter system to a cooler system that are in contact.

We can calculate the heat released or absorbed using the specific heat capacity C, the mass of the substance, m, and the change in temperature, ΔT in the equation:     q=m×C×ΔT

Heat and temperature are two different but closely related concepts. Note that they have different units: temperature typically has units of degrees Celsius (degrees °C,) or Kelvin (K), and heat has units of energy, Joules (J).

Temperature is a measure of the average kinetic energy of the atoms or molecules in the system. The water molecules in a cup of hot coffee have a higher average kinetic energy than the water molecules in a cup of iced tea, which also means they are moving at a higher velocity.5

Temperature is also an intensive property, which means that the temperature doesn't change no matter how much of a substance you have (as long as it is all at the same temperature!). This is why chemists can use the melting point to help identify a pure substance—minus the temperature at which it melts is a property of the substance with no dependence on the mass of a sample.

The equipartition theorem relates the temperature of a system to its average energies. It makes quantitative predictions, provides the total kinetic and potential energies for a system at a given temperature, from which the heat capacity of the system can be calculated. However, the equipartition also provides the average values of individual energy components, such as the kinetic energy of a particular particle or the potential energy of a single spring. For example, it predicts that each atom in an ideal monoatomic gas has an average kinetic energy of (3/2) k B T in thermal equilibrium, where k B is Boltzmann's constant and Te the temperature (thermodynamics).6

Thermal motion of an α-helical peptide. The jittery motion is random and complex and the energy of any particular atom can fluctuate wildly. Nevertheless, the equipartition theorem allows the average kinetic energy of each atom to be computed, as well as the average potential energies of many vibrational modes. The grey, red and blue spheres represent atoms of carbon, oxygen and nitrogen, respectively; the smaller white spheres represent atoms of hydrogen.7

The mole (symbol: mole) is the unit with which the amount of substance is measured, one of the seven fundamental physical magnitudes of the International System of Units.

In any substance (chemical element or compound) and considering at the same time a certain type of elemental entities that make up it, the mole, mole symbol, is the SI unit of quantity of substance. A mole contains exactly 6,022 140 76 × 10–23 elemental entities.8

Kinetic energy is the energy of a moving body. Kinetic energy is defined as the work to be done by the force it exerts on the resting body to accelerate it.9

Development

To begin, we will find the quadratic mean velocity of each molecule of these 4 gases at a temperature of 15°C; the formula is as follows;

 

Nitrogen 78%

R= 8.31 J/mol.k

T= 15+273=288 k

M (N2) = 14.0067 + 14.0067 =28 g/mol

             =0.028kg/mol

Vcm= √ (3 *8, 31 *288)/0.028=

Vcm= √ (24.93 *288)/0.028=

Vcm= √7179.8 / 0.028=506.38 m/s

Oxygen 21%

R= 8.31 J/mol.k

T= 15+273=288 k

M (O2) = 16. + 16 =32 g/mol

             =0.032kg/mol

Vcm= √ (3 *8.31 *288)/0.032=

Vcm= √ (24.93 *288)/0.032=

Vcm= √7179.8/ 0.032= 473.67 m/s

 

Argon 0.934%

R= 8.31 J/mol.k

T= 15+273=288k

M (Ar) = 39.9 =39.9 g/mol

             =0.0399kg/mol

Vcm= √ 3 *8, 31 *288/0.0399=

Vcm= √ (24.93 *288)/0.0399=

Vcm= √ 7179.8 / 0.0399= 424.2 m/s

 

Carbon dioxide (CO2)

R= 8.31 J/mol.k

T= 15+273=288 k

M(CO2)= 12 + 2*16 =44 g/mol

             =0.044kg/mol

Vcm= √3 *8, 31 *288/0.044=

Vcm= √ (24.93 *288)/0.044=

Vcm= √7179.8 / 0.044= 403, 95 m/s

 

Average quadratic speed of the following molecules at 15°C temperature;
GAS	Vcm. Of molecules  at 15°C
Nitrogen               (N2)	506.38 m/s
Oxygen                 (O2)	473.67 m/s
Argón                    (Ar)	424.20 m/s
Carbon dioxide    (CO2)	403.95 m/s.

As the temperature of the atmosphere is a measure of the average kinetic energy of its molecules, then we will find the kinetic energy for each of the 4 main molecules.

Kinetic energy is a form of energy, known as motion energy. The kinetic energy of an object is the energy produced by its mass-dependant movements and speed of the same. Kinetic energy is usually abbreviated by the letters "EC" or "Ek". The word kinetics is of Greek origin “kinesis” meaning “movement”.

Kinetic energy is represented by the following formula: EC=½ mv². Kinetic energy is measured in Joules (J), mass in kilograms (kg) and velocity in meters over seconds (m/s).4 

 

Nitrogen:

M= 0.028kg/mol

V²= 506.38m/s²

Ec= ½ 0.028kg/ mol(*506.38m/s) ²

Ec=3589.89 J

The kinetic energy (E) of a body with mass m = 0.028 kilograms and velocity v = 506.38 m/s equals 3589.89 J

 

Oxygen

M= 0.032kg/mol

V²= 473.67m/s²

Ec= ½ 0.032kg/ mol*(473.67 m/s) ²

Ec= 3589.81 J

The kinetic energy (E) of a body with mass m = 0.032 kilograms and velocity v = 473.67 m/s equals 3589.81 J

 

Argón

M= 0.0399kg/mol

V²= 424.20m/s

Ec= ½ 0.0399kg/ mol*(424.20 m/s) ²

Ec=3589.92 J

The kinetic energy (E) of a body with mass m = 0.0399 kilograms and velocity v = 424.20 m/s equals 3589.92 J

 

Carbón Dioxide   

M= 0.044kg/mol

V²= 403.95m/s

Ec= ½ 0.044kg/ mol*(403.95 m/s) ²

Ec= 3589.86 J

The kinetic energy (E) of a body with mass m = 0.044 kilograms and velocity v = 403.95 m/s equals 3589.86 J

 

Kinetic energy of each mole of the different gases

GAS	kinetic energy (Heat)  at 15°C
Nitrogen                  (N2)	3589.89 J
Oxygen                  (O2)	3589.81 J
Argón                     (Ar)	3589.92 J
Carbón Dioxide    (CO2)	3589.86 J.

 

Parts per million (ppm) is the unit that is frequently used to measure the volume that occupy small amounts of elements (also called traces) within a mixture.

 

The parts per million of the following gases in the atmosphere
GAS	parts per million
Nitrogen                 (N2)	780.800
Oxygen                    (O2)	209.450
Argón                      (Ar)	9.340
Carbón Dioxide    (CO2)	410

 

GAS	VOLUME     PPM	Kinetic energy per Mole gas 15°C	TOTAL(Ek) Mole Gas x Volume 15°C
Nitrogen              (N2)	780.800	3589.89 J	2.802.986.112 J
Oxygen               (O2)	209.450	3589.81 J	751.885.705 J
Argón                  (Ar)	9.340	3589.92 J	33.529.853 J
carbón  Dioxide(CO2)	410	3589.86 J.	1.471.843 J
TOTAL	1.000.000	3589,87 j	3.589.873.512 J

 Now we will find the quadratic mean velocity of each molecule of these 4 gases at a temperature of 14°C;

 

Nitrogen 78%

R= 8.31 J/mol.k

T= 14+273=287 k

M (N2) = 14.0067 + 14.0067 =28 g/mol

             =0.028kg/mol

Vcm= √ (3 *8, 31 *287)/0.028=

Vcm= √ (24.93 *287)/0.028=

Vcm= √7154.9 / 0.028=505.50 m/s

 

Oxygen 21%

R= 8.31 J/mol.k

T= 14+273=287 k

M (O2) = 16. + 16 =32 g/mol

             =0.032kg/mol

Vcm= √ (3 *8.31 *287)/0.032=

Vcm= √ (24.93 *287)/0.032=

Vcm= √7154.9/ 0.032= 472.85 m/s

 

Argon 0.934%

R= 8.31 J/mol.k

T= 14+273=287k

M (Ar) = 39.9 =39.9 g/mol

             =0.0399kg/mol

Vcm= √ 3 *8, 31 *287/0.0399=

Vcm= √ (24.93 *287)/0.0399=

Vcm= √ 7154.9 / 0.0399= 423.46 m/s

 

Carbon dioxide (CO2)

R= 8.31 J/mol.k

T= 14+273=287 k

M (CO2) = 12 + 2*16 =44 g/mol

             =0.044kg/mol

Vcm= √3 *8, 31 *287/0.044=

Vcm= √ (24.93 *287)/0.044=

Vcm= √7154.9 / 0.044= 403, 25 m/s

 

Average quadratic speed of the following molecules at 14°C temperature;
GAS	Vcm. Of molecules  at 14°C
Nitrogen               (N2)	505.50 m/s
Oxygen                 (O2)	472.85 m/s
Argón                    (Ar)	423.46 m/s
Carbon dioxide    (CO2)	403.25 m/s.

Kinetic energy is the energy that a moving body has. Kinetic energy is defined as the work that must be performed by the force it exerts on the resting body to accelerate it:

 

Nitrogen:

M= 0.028kg/mol

V²= 505.50m/s²

Ec= ½ 0.028kg/ mol(*505.50m/s) ²

Ec=3577.42 J

The kinetic energy (E) of a body with mass m = 0.028 kilograms and velocity v = 505.50 m/s equals 3577.42 J

Oxygen

M= 0.032kg/mol

V²= 472.85m/s²

Ec= ½ 0.032kg/ mol*(472.85 m/s) ²

Ec= 3577.39 J

The kinetic energy (E) of a body with mass m = 0.032 kilograms and velocity v = 472.85 m/s equals 3577.39 J

Argón

M= 0.0399kg/mol

V²= 423.46m/s

Ec= ½ 0.0399kg/ mol*(423.46 m/s) ²

Ec=3589.92 J

The kinetic energy (E) of a body with mass m = 0.0399 kilograms and velocity v = 423.46 m/s equals 3577.4 J

Carbón Dioxide   

M= 0.044kg/mol

V²= 403.25m/s

Ec= ½ 0.044kg/ mol*(403.25 m/s) ²

Ec= 3577.43 J

The kinetic energy (E) of a body with mass m = 0.044 kilograms and velocity v = 403.25 m/s equals 3577.43 J 

Kinetic energy of each mole of the different gases

GAS	kinetic energy (Heat)  at 14°C
Nitrogen                  (N2)	3577.42 J
Oxygen                  (O2)	3577.39 J
Argón                     (Ar)	3577.40 J
Carbón Dioxide    (CO2)	3577.43 J.

 

The parts per million of the following gases in the atmosphere
GAS	parts per million
Nitrogen                 (N2)	780.800
Oxygen                    (O2)	209.450
Argón                      (Ar)	9.340
Carbón Dioxide    (CO2)	410

 

GAS	VOLUME     PPM	Kinetic energy per Mole gas 14°C	TOTAL(Ek) Mole Gas x Volume 14°C
Nitrogen              (N2)	780.800	3577.42J	2.793.249.536 J
Oxygen               (O2)	209.450	3577.39J	749.284.335 J
Argón                  (Ar)	9.340	3577.40J	33.412.916 J
carbón  Dioxide(CO2)	410	3577.43J	1.466.746 J
TOTAL	1.000.000	3577,41 j	3.577.410.000 J

 

“If you can measure what you are talking about, and if you can express it by a number, then you may think you know something; but if you can't measure it, your knowledge will be poor and unsatisfactory”

Lord Kelvin

Conclusión

 

GAS	Vcm. Speed Of molecules  at 14°C	Kinetic energy per Mole gas at 14°C	Vcm. Speed Of molecules  at 15°C	Kinetic energy per Mole gas at 15°C
Nitrogen              (N2)	505.50 m/s	3577.42 J	506.38 m/s	3589.89 J
Oxygen               (O2)	472.85 m/s	3577.39 J	473.67 m/s	3589.81 J
Argón                  (Ar)	423.46 m/s	3577.40 J	424.20 m/s	3589.92 J
carbón  Dioxide(CO2)	403.25 m/s.	3577.43 J	403.95 m/s.	3589.86 J.
Average	451.26 m/s	3577,41 J	452.05 m/s	3589.87J

 

We can conclude that the average kinetic energy that originates each mole of gas from the 4 main gases in the atmosphere at 15°C is 3589.87 Joules, and the molecules move to an average of 452.05 m / s, now each mole of gas at 14°C produces a kinetic energy of 3577.41 Joules, and molecules move with an average of 451.26 m/s, this shows us that the heat that molecules in the atmosphere can transfer is greater, when the temperature of the atmosphere increases, and that the increase in the kinetic energy of molecules, is due to an increase in their quadratic velocity. According to this data when a mole of gas molecules in the atmosphere go from 14°C to 15°C, its ability to transfer its energy or heat increases by 12.46Julios, which is an increase by 0.34% in heat for each degree Celsius of temperature increase, and the average speed of molecules increases by 1.24 m/s.

Finally it can be concluded that when the atmosphere increases its temperature by 1 degree centigrade, the heat on the planet increases by 0.34%.

Bibliography

1- Intergovernmental Panel on Climate Change. Consultado el 15 de octubre de 2010.

1.1-https://www.carbonbrief.org/guest-post-why-low-end-climate-sensitivity-can-now-be-ruled-out

1.2-https://advances.sciencemag.org/content/6/26/eaba1981

 A concise description of the greenhouse effect is given in the Intergovernmental Panel on Climate Change Fourth Assessment Report, "What is the Greenhouse Effect?" FAQ 1.3 - AR4 WGI Chapter 1: Historical Overview of Climate Change Science, IIPCC Fourth Assessment Report, Chapter 1, page

2- Maxwell, J. C. (1867). "On the Dynamical Theory of Gases". Philosophical Transactions of the Royal Society of London 157: 49

3-http://www.educaplus.org/gases/ley_charles.html

4-https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/a/heat

5-https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/a/heat

6- http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/eqpar.html

7- https://en.wikipedia.org/wiki/Equipartition_theorem

8-https://es.wikipedia.org/wiki/Mol#cite_note-avogadro-constant-4

9-https://es.calcprofi.com/energia-cinetica-formula-calculadora.html