An ideal gas at pressure P and temperature T is expanding such that PT^3 = constant. The coefficient of volume expansion of the gas is _______.

Step-by-step solution

Given the process equation for the ideal gas: PT^3 = constant From the ideal gas equation, PV = nRT , which gives P = nRT V . Substituting P into the process equation: ( nRT V ) T^3 = constant T^4 V = constant V = k T^4 Differentiating both sides with respect to temperature T : dV dT = 4k T^3 The coefficient of volume expansion is defined as: = 1 V dV dT Substituting the values of V and dV dT : = 1 k T^4 (4k T^3) = 4 T Answer: 4 T