Question

(a) Apply Maxwell relation and Gibb’s first equation (du=TdS-Pdv) to find the (∂u/∂P)_Trelation in terms of directly measurable properties (P, V and T). For an ideal gas, what will be the value of that partial derivative?

(b) Illustrate physical meaning of Inversion line with the help of T-P diagram.

(C) Assume that carbon dioxide (CO2) is collected from bacterial decomposition of organic matter at 5℃, and atmospheric pressure (100 kPa), and is required to be used in a process at -30℃, 40 bar. Apply theory of real gas behavior to calculate how much actual minimum work input and heat transfer is required to reach this state. Also, suggest some devices that can be used to obtain this state change

Answer 1

b)

Constant-enthalpy lines on the T-P diagram pass through a point of zero slope or zero Joule-Thomson coefficient. The line that passes through these points is called the inversion line, and the temperature at a point where a constant-enthalpy line intersects the inversion line is called the inversion temperature.

Above graph shows different isenthalpic (throttling) curves. Each curve has its own maxima.By observing the above isenthalpic curves, we can easily say that throttling will only result in cooling when the slope of the curve is positive.And if the initial temperature of the fluid (used in throttling) is above maximum inversion temperature, then we can never get cooling.To have maximum cooling the initial state of fluid should lie at inversion curve.The locus of maxima of these isenthalpic curves is known as inversion curve.

The slope of isenthalpic (throttling) T- P curves is known as Joule Thomson coefficient.

Here one should know that Joule Thomson coefficient, Joule Thompson coefficient, Joule Kelvin coefficient are the different names of the same thing.

Joule Thomson coefficient is represented as μ_J.

μ_J = (∂T/∂P)_h

For ideal gases

μ_J = (∂T/∂P)_h = 0 (inversion line)

It means we can never heat or cool ideal gas by throttling.

a)