Query: An exponential increase in CO2 will result in a linear increase in temperature

Relevant passages:
Soil respiration <=SEP=> Soil respiration refers to the production of carbon dioxide when soil organisms respire . This includes respiration of plant roots , the rhizosphere , microbes and fauna .   Soil respiration is a key ecosystem process that releases carbon from the soil in the form of CO2 . CO2 is acquired from the atmosphere and converted into organic compounds in the process of photosynthesis . Plants use these organic compounds to build structural components or respire them to release energy . When plant respiration occurs below-ground in the roots , it adds to soil respiration . Over time , plant structural components are consumed by heterotrophs . This heterotrophic consumption releases CO2 and when this CO2 is released by below-ground organisms , it is considered soil respiration .   The amount of soil respiration that occurs in an ecosystem is controlled by several factors . The temperature , moisture , nutrient content and level of oxygen in the soil can produce extremely disparate rates of respiration . These rates of respiration can be measured in a variety of methods . Other methods can be used to separate the source components , in this case the type of photosynthetic pathway ( C3/C4 ) , of the respired plant structures .   Soil respiration rates can be largely affected by human activity . This is because humans have the ability to and have been changing the various controlling factors of soil respiration for numerous years . Global climate change is composed of numerous changing factors including rising atmospheric CO2 , increasing temperature and shifting precipitation patterns . All of these factors can affect the rate of global soil respiration . Increased nitrogen fertilization by humans also has the potential to effect rates over the entire Earth .   Soil respiration and its rate across ecosystems is extremely important to understand . This is because soil respiration plays a large role in global carbon cycling as well as other nutrient cycles . The respiration of plant structures releases not only CO2 but also other nutrients in those structures , such as nitrogen . Soil respiration is also associated with positive feedbacks with global climate change . Positive feedbacks are when a change in a system produces response in the same direction of the change . Therefore , soil respiration rates can be effected by climate change and then respond by enhancing climate change .

Creep (deformation) <=SEP=> In materials science , creep ( sometimes called cold flow ) is the tendency of a solid material to move slowly or deform permanently under the influence of mechanical stresses . It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material . Creep is more severe in materials that are subjected to heat for long periods , and generally increases as they near their melting point .   The rate of deformation is a function of the material properties , exposure time , exposure temperature and the applied structural load . Depending on the magnitude of the applied stress and its duration , the deformation may become so large that a component can no longer perform its function -- for example creep of a turbine blade will cause the blade to contact the casing , resulting in the failure of the blade . Creep is usually of concern to engineers and metallurgists when evaluating components that operate under high stresses or high temperatures . Creep is a deformation mechanism that may or may not constitute a failure mode . For example , moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that might otherwise lead to cracking .   Unlike brittle fracture , creep deformation does not occur suddenly upon the application of stress . Instead , strain accumulates as a result of long-term stress . Therefore , creep is a `` time-dependent '' deformation .

Virial expansion <=SEP=> The classical virial expansion expresses the pressure of a many-particle system in equilibrium as a power series in the number density .  The virial expansion , introduced in 1901 by Heike Kamerlingh Onnes , is a generalization of the ideal gas law . He wrote that for a gas containing atoms  or molecules ,   where is the pressure , is the Boltzmann constant , is the absolute temperature , and  is the number density of the  gas .  Note that for a gas containing a fraction of ( Avogadro 's number ) molecules , truncation of the virial expansion after the  first term leads to , which is the ideal gas law .   Writing , the virial expansion can be written as   .   The virial coefficients are characteristic of the interactions between the particles in the system and in general depend on the temperature . Virial expansion can also be applied to aqueous ionic solutions , as shown by Harold Friedman .