An Introduction to Thermal Physics · Problem 4.34
Engines and Refrigerators — Daniel Schroeder
Physics — Statistical Mechanics · ideal-hampson-linde-cycle
Problem
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 be the fraction of the fluid that liquefies on each pass through the cycle. Show that where is the enthalpy of each mole of compressed gas that goes into the heat exchanger, is the enthalpy of each mole of low-pressure gas that comes out of the heat exchanger, and 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 the 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 an input temperature of 200 K.Intuitive explanation
The Hampson-Linde cycle liquefies gas by exploiting the Joule-Thomson effect—the fact that real gases cool when throttled at constant enthalpy. The key insight is that enthalpy is conserved through the throttling valve and heat exchanger together: high-pressure gas enters with enthalpy , and the mixture exiting (some liquid, some gas) has the same total enthalpy. By tracking how enthalpy splits between the liquid and gas phases, you can find what fraction must condense to balance the energy budget. Lower input temperatures favor liquefaction because the gas starts closer to its condensation point.
Intuitive explanation
The Hampson-Linde cycle liquefies gas by exploiting the Joule-Thomson effect—the fact that real gases cool when throttled at constant enthalpy. The key insight is that enthalpy is conserved through the throttling valve and heat exchanger together: high-pressure gas enters with enthalpy , and the mixture exiting (some liquid, some gas) has the same total enthalpy. By tracking how enthalpy splits between the liquid and gas phases, you can find what fraction must condense to balance the energy budget. Lower input temperatures favor liquefaction because the gas starts closer to its condensation point.