Typical temperatures (T) and pressures (p) and speeds (v) in a De Laval Nozzle. The large bell or cone shaped expansion nozzle gives a rocket engine its characteristic shape.
In rockets the hot gas produced in the combustion chamber is permitted to escape from the combustion chamber through an opening (the "throat"), within a high expansion-ratio 'de Laval' nozzle.
Provided sufficient pressure is provided to the nozzle (about 2.5-3x above ambient pressure) the nozzle chokes and a supersonic jet is formed, dramatically accelerating the gas, converting most of the thermal energy into kinetic energy.
The exhaust speeds vary, depending on the expansion ratio the nozzle is designed to give, but exhaust speeds as high as ten times the speed of sound of sea level air are not uncommon.
Rocket thrust is caused by pressures acting in the combustion chamber and nozzle. From Newton's third law, equal and opposite pressures act on the exhaust, and this accelerates it to high speeds.
About half of the rocket engine's thrust comes from the unbalanced pressures inside the combustion chamber and the rest comes from the pressures acting against the inside of the nozzle (see diagram). As the gas expands (adiabatically) the pressure against the nozzle's walls forces the rocket engine in one direction while accelerating the gas in the other.