  The effective field theory motivated relativistic mean-field (E-RMF)
formalism is employed to study the equation of state (EoS) for the infinite
symmetric nuclear matter at finite temperature using the recently developed
forces FSUGarnet, IOPB-I, G3, and the well known NL3 force parameter. The EoS
is then used to estimate the critical temperature $T_c$, pressure $P_c$ and
density $\rho_c$ of the symmetric nuclear matter for the liquid-gas phase
transition. As $T_c$ is not a constrained parameter in both experiments and
theoretical calculations, there is a large uncertainty around its value.
Although, the critical parameters are correlated among themselves. It is
revealed that vector self-coupling $\zeta_0$ of used forces play determining
role in EoS in finite temperature limit. Keeping the incompressibility in
acceptable limit i.e. 240$\pm$ 20 MeV, the lower value of $\zeta_0$ gives a
better result of $T_c$ when compared to the several experimental data. The
critical parameters however show weak correlation with the properties at
saturation density at zero temperature. The compressibility factors calculated
with these parameters are in agreement with the universal value of liquid-gas
systems. Stability conditions are examined along with binodal and spinodal
regions. Besides this, the thermodynamic properties like specific heat and
latent heat are also worked out. We have carried out detailed consistency check
of our calculations using critical exponents and standard scaling laws. All the
exponents are well within the theoretical mean-field results.
