  The theory of equilibrium phase transition, which traditionally does not
involve time evolution, concerns only static quantities. In recent decades,
owing to the development of nonequilibrium thermodynamics, there is a growing
interest in nonequilibrium phase transition which concerns time evolution. It
is well-known that in the absence of phase transitions, the excess work
resulted from finite-rate quench is proportional to the quench rate v. The time
evolution in a second-order phase transition can be understood via the
Kibble-Zurek mechanism, and the scaling of work is related to the critical
exponents. Nevertheless, the finite-time nonequilibrium thermodynamics of the
first-order phase transition remains largely unexplored. We investigate the
scaling relations of some thermodynamic quantities with the quench rate in the
first-order phase transition. It is shown that the excess work scales as
$v^{2/3}$ for small quench rate. Moreover, the delay time and the transition
time scale as $v^{1/3}$. Our study deepens the understanding about the
nonequilibrium thermodynamics of the first-order phase transition.
