The polytropic exponent (of a polytrope) has been shown to be equivalent to the pressure derivative of the bulk modulus where its relation to the Murnaghan equation of state has also been demonstrated. The polytrope relation is therefore best suited for relatively low-pressure (below 10 Pa) and high-pressure (over 10 Pa) conditions when the pressure derivative of the bulk modulus, which is equivalent to the polytrope index, is near constant.