A gas, initially at T-500 K, undergoes a Joule-Thompson (constant enthalpy) expansion from P=10 atm to P=1 atm. 1. A) Prove that (dT/dP) is equal to: (1/Cp)[T(dV/dT)p - V] (You may assume this expression is valid for parts B and C, even if you are unable to prove it.) 1. B) Find an expression for (dV/dT)p for this gas, in terms of P, T and known constants, assuming it follows the equation of state: V = (RT/P) + aTp For full credit your answer should be an algebraic equation-all derivatives should be evaluated. 1. C) Assuming the heat capacity of the gas is constant at C-5R, and that a=2x107 L mol K-atm, find the final temperature of the gas. Write (OT/OP) from part A) in terms of P and evaluate to find the final temperature of the gas.

A gas, initially at T=500K, undergoes a Joule-Thompson (constant enthalpy) expansion from P=10atm to P=1atm. 1. A) Prove that (dT/dP)H is equal to: (1/Cp)[T(dV/dT)pV] (You may assume this expression is valid for parts B and C, even if you are unable to prove it.) 1. B) Find an expression for (dV/dT)P for this gas, in terms of P,T and known constants, assumingit follows the equation of state: V=(RT/P)+aT2P2 For full credit your answer should be an algebraic equation-all derivatives should be evaluated. 1. C) Assuming the heat capacity of the gas is constant at Cp=5R, and that a =2107Lmol1K2atm2. find the final temperature of the gas. Write (T/P)H from part A) in terms of P and evaluate to find the final temperature of the gas