  The paper contains an extensive study of the unified first law (UFL) in the
Friedmann-Robertson-Walker spacetime model. By projecting the UFL along the
Kodama vector the second Friedmann equation can be obtained. Also studying the
UFL on the event horizon it is found that Clausius relation cannot be obtained
from the UFL by projecting it along the tangent to the event horizon as it can
be for the trapping horizon. However, it is shown in the present work that
Clausius relation can be obtained by projecting the UFL along the Kodama vector
on the horizon and the result is found to be true for any horizon. Finally
motivated by the Unruh temperature for the Rindler observer, surface gravity is
redefined and a Clausius relation is obtained from the UFL by projecting it
along a vector analogous to the Kodama vector.
