An ideal gas undergoes a thermodynamic process such that its volume expansion coefficient varies with absolute temperature T as = 2 T . The process equation for the gas in terms of pressure P and volume V is :

Step-by-step solution

The volume expansion coefficient is defined as = 1 V dV dT . Given that = 2 T , we can write: 1 V dV dT = 2 T Integrating both sides: dV V = 2 T dT V = 2 T + C V = (T^2) + C V = k T^2 T = V k Using the ideal gas equation, PV = nRT : P = nRT V Substituting the expression for T : P = nR V V k = nR k V^ -1/2 P V^ 1/2 = constant Squaring both sides, we get the process equation: P^2 V = constant Answer: P^2 V = constant