An ideal gas undergoes a thermodynamic process such that its pressure P and absolute temperature T are related by the equation P = T^3 , where is a positive constant. The gas transitions from an initial state (P₁, V₁, T₁) to a final state (P₂, V₂, T₂) . Which of the following statements is correct?

Step-by-step solution

Given the process equation P = T^3 . From the ideal gas equation, PV = nRT , we can write T = PV nR . Substituting T into the given equation: P = ( PV nR )^3 P = P^3 V^3 n^3 R^3 P^2 V^3 = n^3 R^3 = constant P 1 V^ 3/2 This shows that pressure and volume are inversely related. If pressure decreases, volume must increase. Therefore, if P₂ V₁ . We can also check the other relations: V = nRT P = nRT T^3 = nR T^2 V 1 T^2 Thus, volume and temperature are inversely related. If T₂ > T₁ , then V₂ Since P = T^3 , pressure an