Analyzing the given statements:
Statement I: At constant pressure, physical adsorption decreases with increase in temperature. This is correct because physical adsorption is an exothermic process and its efficiency decreases as the temperature increases.
Statement II: Enthalpy of physisorption is higher than enthalpy of chemisorption. This is incorrect because chemisorption involves a chemical bond formation, which has higher enthalpy compared to physical adsorption.
Statement III: Gas masks used in coal mines consist of activated charcoal. This is correct because activated charcoal is used in gas masks due to its adsorption properties to remove harmful gases.
Thus, the correct statements are I and III.