An ideal gas expands in such a way that its pressure is directly proportional to the cube of its density. During this expansion process, the temperature of the gas:

Step-by-step solution

Let the pressure of the gas be P , volume be V , and density be . Given that P ^3 . Since the mass of the gas is constant, density is inversely proportional to volume ( 1 V ). Therefore, P 1 V^3 , which can be written as PV^3 = constant . From the ideal gas equation, PV = nRT , we can substitute P = nRT V . Substituting this into the process equation: ( nRT V ) V^3 = constant T V^2 = constant This implies that T 1 V^2 . As the gas expands, its volume V increases. Since temperature is inversely proportional to the s