Gas Turbines

http://en.wikipedia.org/wiki/Brayton_cycle

The air is heated after pressurizing to increase the volume and thus the energy available to extract with the turbine. No, the heating does not increase the pressure. That can occur with engines that contain the air in a controlled volume. Burning the gas/air mixture is a common way to heat the mixture.

See post #1

But by increasing the volume won't that be increasing the pressure as the Combustor and Turbine is a set volume

No, it will not increase the pressure, because the "set volume" you are describing is not physically closed by pressure-insensitive "walls". The turbine blades on the compressor and the turbine are "open", which means that the amount of material passing through them is a variable function dependent on pressure, temperature, and flow rate. Try imagining what a molecule (or molecular bundle) would do as it moves through the system. An understanding of how gases interact with airfoils (or turbine blades) is an important part of how turbines work. When we speak of increasing or decreasing pressure, we are speaking macroscopically, not microscopically. This means that macro is describing the generalized or average pressure, micro involves the pressures at individual points, with variations dependent on the turbulence in the gas stream, flow resistance, individual molecular velocity variations, chemical reactions and the subsequent energy dispersions, and the mechanical interaction with the foils and walls of the gas stream. The gas turbine, unlike a piston engine, is not a piece-by-piece process of a specific mass of reactants, but is a continuous flow of reactants, with the entire stream connected in the reacting interaction. This means that the instantaneous reaction of each molecule of fuel, or each increase of thermal energy, no matter how it is introduced into the gas stream, is affecting the whole system of energy transformation from heat to mechanical energy. This is speaking from the macro viewpoint. The micro viewpoint also involves relatively subtle transmissions of force and energy through the gas stream (like sound waves-which of course vary in speed depending on the conditions), though the results constitute the macro viewpoint.

The whole point of the compressor stage is the production of pressure. The combustion or heating stage is essentially a constant pressure process. Have you looked at the Brayton cycle link?