I am sorry if this question is dumb but can we apply the first law of thermodynamics directly on atoms?
I've say an ion and I'm adding an electron to it, can I write anything like $$d U=d Q-d W$$ to this process,which is related to the first law of thermodynamics?
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing two kinds of transfer of energy, as heat and as thermodynamic work, and relating them to a function of a body's state, called Internal energy.
italics mine.
Thermodynamics is a theory developed on the same basic laws as all of physics theories, including conservation of energy, but its variables are defined over a statistical ensembles of particles, as was made clear with the statistical form of thermodynamics..
A single atom also obeys the law of conservation of energy, but not in terms of thermodynamic variables, which apply on statistical ensembles. One atom does not make a statistical ensemble.
I agree with @anna v answer.
To illustrate that thermodynamics applies to "statistical ensembles" consider the property of temperature, $T$.
The kinetic temperature of a substance is a measure of the average translational kinetic energy molecules of that substance. The speed, and thus kinetic energy, of individual molecules of a substance having a certain temperature will vary about the average. In the case of an ideal gas, the distribution of the speeds and thus kinetic energy of the molecules is given by the Maxwell Speed Distribution, as shown in the third panel of the following link: http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kintem.html#c1
Suppose, for example, we were to remove a random sample of molecules from the ensemble, isolated it, and measure its temperature. We may find that its temperature deviates considerably from that of the ensemble because the deviation of its average kinetic energy from the ensemble. The smaller the sampling of the molecules of the ideal gas the greater the potential deviation of the average kinetic energy and "temperature" of that sample from that of the ensemble. If the sample reaches the level of a single molecule, and it happened to be a molecule having a speed corresponding to the head or tail of the Maxwell distribution, the "temperature" of that molecule would obviously have no relationship to the temperature of the ensemble of molecules.
Hope this helps.
