Hi Peter, thanks for your reaction.
Heating and cooling proceses The temperature in molecular clouds is set mostly by radiative processes - adiabatic heating and cooling associated with hydrodynamic motions is generally negligible, as we will show in a moment.
Thus we have to consider how clouds can gain and loose heat by radiation. A full treatment of this problem necessarily involves numerical calculations, but we can derive some basic results quite simply.
Heating by cosmic rays In the bulk of the interstellar medium the main source of heating is starlight. Thus, we can generally neglect starlight as a source of heat except very near young stars forming within the cloud.
Instead, over the bulk of a molecular cloud's volume, the main source of heating is cosmic rays: How much heat do cosmic rays produce? To answer this question, we must first determine the mechanism by which the gas is heated.
The first step in such a heating chain is the interaction of a cosmic ray with an electron, which knocks the electron off a molecule: The electron cannot easily transfer its energy to other particles in the gas directly, because its tiny mass guarantees that most collisions are elastic and transfer no energy to the impacted particle.
However, the electron also has enough energy to ionize or dissociate other hydrogen molecules, which provides an inelastic reaction that can convert some of its 30 eV to heat. Secondary ionizations do indeed occur, but in this case almost all the energy goes into ionizing the molecule Instead, it is secondary dissociations and excitations that wind up being the dominant energy channels.
The former reaction is 39 In this reaction any excess energy in the electron beyond what is needed to dissociate the molecule 4.
Alternately, an electron can hit a hydrogen molecule and excite it without dissociating it.
The hydrogen molecule then collides with another hydrogen molecule and collisionally de-excites, and the excess energy again goes into recoil, where it is efficiently shared.
The reaction is 40 41 Summing over all possible transfer channels, and including heating by secondary ionizations too, the energy yield per primary cosmic ray ionization is in the range eV [ 1011 ], depending on the density.
These figures are slightly uncertain. CO cooling In molecular clouds there are two main cooling processes: Dust can cool the gas efficiently because dust grains are solids, so they are thermal emitters.
However, dust is only able to cool the gas if collisions between dust grains and hydrogen molecules occur often enough to keep them thermally well-coupled. Otherwise the grains cool off, but the gas stays hot. The density at which grains and gas become well-coupled is around cm-3 [ 13 ], which is higher than the typical density in a GMC, so we won't consider dust cooling further at this point.
We'll return to it in the next section when we discuss collapsing objects, where the densities do get high enough for dust cooling to be important. The remaining cooling process is line emission, and by far the most important molecule for this purpose is CO, due to its abundance and its ability to radiate even at low temperatures and densities.Before we begin, life will be a bit easier if we re-write the entire second equation in a manifestly tensorial form - this simplifies the analysis tremendously.
To do so, we define two tensors: the fluid pressure tensor and the Maxwell stress tensor T M, as follows. 5. Aqueous phase chemistry. The pH of water is defined as pH = - log 10 [H +], and is at K. When pH is less than 7, the solution is acidic.
If initially there was no cloud, then the conservation equation for H 2 O 2 becomes. Understand r-bridal.comss file configuration One of our main goals is to configure Bitnami applications in the most secure way. For this reason, we moved the configuration in r-bridal.comss files to the main application configuration files and set the AllowOverride option to None by default..
NOTE: The Apache Software Foundation also recommends this configuration. A nucleophile is a species that donates an electron pair to an electrophile to form a chemical bond in a reaction.
All molecules or ions with a free pair of electrons can act as nucleophiles. Because nucleophiles donate electrons, they are by.
Feb 15, · Re: Create logarithmic equation from excel chart I don't know if using a trendline is going to work.
It is a smooth concave shaped curve and the trendline is straight. Using an equivalence to solve equations. The fact that the exponential equation \(y = b^x\) is equivalent to the logarithmic equation \(x = \log_by\) may be used to solve some exponential and logarithmic equations.