  Internal shocks between propagating plasma shells, originally ejected at
different times with different velocities are believed to play a major role in
dissipating the kinetic energy, thereby explaining the observed lightcurve and
spectra in a large range of transient objects. Even if initially the colliding
plasmas are cold, following the first collision the plasma shells are
substantially heated, implying that in a scenario of multiple collisions, most
collisions take place between plasmas of non-zero temperatures. Here, we
calculate the dynamical properties of plasmas resulting from collision between
arbitrarily hot plasma shells, moving at arbitrary speeds. We provide simple
analytical expressions valid for both the ultra-relativistic and Newtonian
velocities, for both hot and cold plasmas. We derive the minimum criteria
required for the formation of the two-shock wave system, and show that in the
relativistic limit, the minimum Lorentz factor is proportional to the square
root of the ratio of the initial plasmas enthalpies. We provide basic scaling
laws of synchrotron emission from both the forward and reverse shock waves, and
show how these can be used to deduce the properties of the colliding shells.
Finally, we discuss the implications of these results in the study of several
astronomical transients, such as x-ray binaries, radio load quasars and
gamma-ray bursts.
