Let's consider the case of a compressor operating at a certain point. Hypothetically, if this compresson is not attached anywhere it will start moving backwards, as a result of the force due to the pressure difference on its 2 sides. In this occasion, the electrical energy that the compressor consumes is converted into gas energy (increase in its enthalpy) and kinetic energy of the compressor. So, if this is true there is always a big piece of the mechanical energy of the compressor converted into kinetic energy (even if it is attached on the earth, theoritecally it slightly increases earth's kinetic energy). I am very confused because I have been teached that the electricity that a compressor consumes is equal to E=mgas(h2-h1)/hm* where mgas the mass of the incoming gas, (h2-h1) the difference in enthalpy of the gas and hm the mechanical efficiency of the machine. Where is this false?

Let's consider the case of a compressor operating at a certain point. Hypothetically, if this compresson is not attached anywhere it will start moving backwards, as a result of the force due to the pressure difference on its 2 sides. In this occasion, the electrical energy that the compressor consumes is converted into gas energy (increase in its enthalpy) and kinetic energy of the compressor. So, if this is true there is always a big piece of the mechanical energy of the compressor converted into kinetic energy (even if it is attached on the earth, theoritecally it slightly increases earth's kinetic energy). I am very confused because I have been teached that the electricity that a compressor consumes is equal to $E=m_{\mathrm{gas}}\cdot(h_2-h_1)/h_m$ where $m_{\mathrm{gas}}$ the mass of the incoming gas, $(h_2-h_1)$ the difference in enthalpy of the gas and $h_m$ the mechanical efficiency of the machine. Where is this false?