In 1929, Hubble observed that the universe is expanding. The expansion is explainable by cosmic extensions presented by Friedmann. Recently, Padmanabhanshowed that expansion of space is related to difference of degrees of freedom on the holographic surface and the number of degrees of freedom in the interior volume. By applying this principle, we can retrieve Einstein field equations which are for explaining fundamental gravitational interactions occurred because of space-time curvature due to existence of matter or energy. This principle can be also used to obtain the dynamic equations of the universe for generalized gravities. In 1996, Jacobson achieved the Einstein equations by applying Clausiusrelation and equivalence principle. In this thesis, we study the origin of dynamic relation which is governing the expansion of the space, and also it has been shown that we can retrieve the dynamic relation by the first law of thermodynamics and vice versa. Therefore, by having one of the three equations, the first law of thermodynamics, the dynamic equation of the universe and the dynamic relation governing the expansion of the space, the other two equations can be derived. In addition, by applying the dynamic relation which is governing the expansion of space and is actually the first law of thermodynamics, we achieve Friedmann equations for generalized gravities like f(R) gravity and scalar-tensor gravity. Furthermore, we discuss and obtain geodesics in thermodynamic geometry of some black holes and also ideal gas.