Adiabatic and isothermal propagations of spherical blast wave produced due to a nuclear explosion have been studied using the Energy hypothesis of Thomas, in the nonuniform atmosphere of the earth. The explosion is considered at different heights. Entropy production is also calculated along with the strength and velocity of the shock. In both the cases; for adiabatic and isothermal flows, it has been found that shock strength and shock velocity are larger at larger heights of explosion, in comparison to smaller heights of explosion. Isothermal propagation leads to a smaller value of shock strength and shock velocity in comparison to the adiabatic propagation. For the adiabatic case, the production of entropy is higher at higher heights of explosion, which goes on decreasing as the shock moves away from the point of explosion. However for the isothermal shock, the calculation of entropy production shows negative values. With negative values for the isothermal case, the production of entropy is smaller at higher heights of explosion, which goes on increasing as the shock moves away from the point of explosion. Directional study of the shock motion and entropy production show that in both the cases of adiabatic and isothermal flow, shock strength and shock velocity are larger in upward motion of the shock, in comparison to the downward motion of the shock. For adiabatic flow, entropy production is larger in upward motion of the shock; whereas, with negative values, entropy production is smaller in upward motion of the isothermal shock. For the adiabatic case, the profiles of shock strength, shock velocity and entropy production are smooth and have the largest value in vertically upward direction and have the lowest value in vertically downward direction, forming the oval shape. For the isothermal case, the profiles of shock strength and shock velocity show similar trend as that for adiabatic case but the profile of entropy production shows opposite trend. The profiles maintain their shape as the shock moves away. Comparison with observed values of shock velocity shows that isothermal case produces better results in comparison to the adiabatic case.