P × V — Page 206, Lesson 276

Let me start by giving you the foundation for this whole chapter, because everything in gas turbine theory hangs on one simple relationship. We have the equation P × V over T equals K. Let me unpack that symbol by symbol. P is pressure, V is volume, T is absolute temperature, and K is a constant. So the product of pressure and volume of the air, divided by the absolute temperature, stays constant throughout the working cycle. Another way to say it: the product of pressure and volume at any stage is proportional to the absolute temperature of the air at that stage. Now, the three main stages where these conditions change are compression, combustion, and expansion. Let's walk through each one. During compression, work is done to increase the pressure and decrease the volume of the air. And there's a corresponding rise in its temperature. Now here's the practical payoff: higher compression ratios give higher thermal efficiency and low specific fuel consumption. That's a key design driver — why engineers push compression ratios up. But there's a catch with outside air temperature. A decrease in outside air temperature will increase the density of the air. Denser air means the compressor has to work harder on it. And how do you see that in the cockpit? It shows up as a drop in engine rpm — unless the fuel control unit compensates for it. So cold day, denser air, compressor works harder, rpm tends to drop. Now during combustion. We add fuel to burn with the air. That increases the temperature, and there's a corresponding rise in volume — but at an almost constant pressure. So combustion is roughly a constant-pressure process. Then during expansion. Some of the energy in the gas stream is being converted to mechanical energy by the turbine. Here there's a decrease in pressure and temperature of the gas, with a corresponding increase in its volume. So you can see the pattern: compression squeezes, combustion heats, expansion lets it grow and do work. And these changes in temperature, pressure, and velocity of the gas through the engine are all shown in Figure 13.5, which traces them through a single spool axial flow engine. That's the core of the gas turbine working cycle — the P×V/T relationship governing compression, combustion, and expansion.