Chapter 4.4, Problem 34P

Consider an ideal Hampson-Linde cycle in which no heat is lost to the environment.

(a) Argue that the combination of the throttling valve and the heat exchanger is a constant-enthalpy device, so that the total enthalpy of the fluid coming out of this combination is the same as the enthalpy of the fluid going in.

(b) Let x be the fraction of the fluid that liquefies on each pass through the cycle. Show that $x=\frac{H_{out}-H_{in}}{H_{out}-H_{liq}}$, where $H_{in}$ is the enthalpy of each mole of compressed gas that goes into the heat exchanger, $H_{out}$ is the enthalpy of each mole of low-pressure gas that comes out of the heat exchanger, and $H_{liq}$ is the enthalpy of each mole of liquid produced.

(c) Use the data in Table 4.5 to calculate the fraction of nitrogen liquefied on each pass through a Hampson-Linde cycle operating between 1 bar and 100 bars, with an input temperature of 300 K. Assume that the heat exchanger works perfectly, so that temperature of the low-pressure gas coming out of it is the same as the temperature of the high-pressure gas going in. Repeat the calculation for input temperature of 200 K.