Consider the equation-of-state you have been working with. a.) A common evaluati
ID: 3279261 • Letter: C
Question
Consider the equation-of-state you have been working with. a.) A common evaluation of EoS's is the measure of the ability to compress the gas under isothermal conditions. The parameter, "isothermal compressibility" is used for this and is defined as: K_T = -1/V middot (partial differential V/partial differential P)_T Derive an expression for K_T for this gas. b.) In lecture, without derivation, it was stated that the change in the internal energy w.r.t. volume can be determined from an equation-of-state via: (partial differential U/partial differential V)_T = T middot (partial differential P/partial differential T)_v - P Derive an expression for the internal energy change w.r.t. volume for the equation of state given c.) Explain why you obtained the result you did.Explanation / Answer
a) Equation of state: PV = nRT, so V = nRT/P
Partial derivative dV/dP = -nRT/ P2 = -V/P, so isothermal compressibility, Kt = 1/P
b) Also partial derivative dP/dT = nR/V = P/T,
partial derivative dU/dV = 0, i.e. internal energy is independent of volume
c) Clearly the ideal gas is the one which has no intermolecular interactions and so internal energy is dependent on kinetic and potential energies of molecules.