  We examine the evolution of universe in $f(R,T)$ gravity where $R$ is the
Ricci curvature and $T$ is the trace of energy momentum tensor. We focus on the
specific form $f(R,T) = R+f(T)$ and explicitly find out the relation between
$f(T)$ and state of equation $w$ by adiabatic condition. All possible modes of
evolution of the scale factor for the five kinds of state of equation, $w= \pm
1, \pm 1/3, 0$ are exhibited. We simulate numerically the plots of redshift
versus distance modulus for three interesting modes and then obtain the good
fitting curve compared with the astronomical observation data.
