An ideal gas is expanding such that P T^2= constant. The coefficient of volume expansion of the gas is

Step-by-step solution

The equation of state for an ideal gas is PV = nRT . Given PT² = C , where C is a constant, we can write P = C T⁻² . Substituting this into the ideal gas equation, we get (C T⁻²) V = nRT . Rearranging for V , we have V = nR C T³ . The coefficient of volume expansion is defined as = 1 V ( dV dT )_ P . Differentiating V with respect to T from the relation V = nR C T³ , we get dV dT = 3 nR C T² . Substituting V and dV dT into the expression for : = 1 ( nR C T³ ) ( 3 nR C T² ) = 3 T . Answer: 3 T