Geophysical conditions are now understood to play a key role on the habitability of extrasolar planets. Studies on the geological time evolution of magnetic fields, crustal chemistry and the atmosphere of rocky extrasolar planets are relevant in this context. These phenomena are influenced by the evolution of internal heat and volcanism of these planets. In this paper we will be presenting our investigations on the geological time evolution of volcanism in 53 potentially habitable extrasolar planets in our galaxy based up our model extrapolating our geophysical knowledge of rocky planets in the inner solar system. We will also explain how the results of this study will influence the habitability of these extrasolar planets. Volcanism is known to be an important dissipation mechanism of internal heat in rocky planetary objects like Earth. Different aspects of volcanism in the inner solar system are studied extensively. There are models which address the time evolution of volcanism in rocky extrasolar planets. The phenomenon of cessation of volcanism in planetary objects is not understood in detail so far. In our model we suggested that the major volcanism in the Earth will cease in the near geological future based on the critical internal value needed to sustain volcanic /tectonic activity in rocky solar system planetary objects.The time evolution of volcanism in Earth and Mars has probably influenced the origin of life and biological evolution in these planets. Planetary mass possibly decides its thermal and volcanic history over geological time scales .The current internal heat parameters inferred for inner solar system planetary objects is found to be proportional to the basic geophysical properties of these planetary objects such as mass. In this context we also could find a planetary mass-volcanic cessation age relation from our model. This relation is supported by the inferences of cessation ages of inner solar system planetary objects. For the case of Earth, we have also found a linear regression relation between surface heat flux and maximum intensity of volcanism using relevant observations during the past 200 Myrs.The results of our geophysical studies of inner solar system and its comparison with the known features of biological evolution in Earth are extrapolated to 53 PHESP to find its internal heat and volcanism at specific geological ages. The tidal heat contributions to the internal heat of extrasolar planets due to the influence of host star is also inferred in this context. From the host star ages, around 10 extrasolar planets (majority are Kepler candidates) out of 53 is found to be at present in the declining phase of volcanism which is suggested to be the best period for origin of lifeforms in these extrasolar planets. The time evolution of volcanism and its possible role in the habitability of selected extrasolar planets like will be also discussed in detail in this context. In addition to this we also study the dynamical interactions of extrasolar planets with its host star to know about the stellar activity variations of the host star of extrasolar planets which will affect the habitability conditions of the extrasolar planets.