In thermodynamics, the Joule-Thomson effect describes a process in which a fluid is forced through a valve or porous plug while kept insulated so that no heat is exchanged with the environment. This procedure is called a throttling process or Joule-Thomson process. The rate of change of temperature T with respect to pressure P in a Joule-Thomson process (that is, at constant enthalpy H) is the Joule-Thomson coefficient µJT.

(a) Find a relationship between  µJT , Cp and β (volumetric coefficient of thermal expansion)

Hint : The final relationship will also include T and V)

(b) What is the value of µJT for an ideal gas?

(c) Air flows at a steady rate through a horizontal insulated pipe which contains a partially closed valve. The conditions of the air upstream from the value of 50 ºC and 5.5 bar, and the downstream pressure is 2.5 bar.  If the air is regarded as an ideal gas, what is the temperature of the air some distance downstream from the valve? Assume the change of kinetic energy of the air is negligible.  Recall that for throttling process H is constant.