The velocity of sound in a gas increases as the square root of the absolute temperature.
So, if you have a resonant exhaust such as the classic twin cone 2-stroke exhaust the rpm at which resonance is reached increases as the temperature of the gasses in the exhaust increase and this increases slightly as the wall temperature of the exhaust increases. However, the residence time of the gasses in the exhaust is usually short enough that the gasses do not get anywhere near equilibrium with the walls and the gas temperature is significantly higher than the exhaust walls. This rather complicates matters when it comes to designing the exhaust.
As for changes in the speed of flow of the gasses from the exhaust there are two other factors:-
The volume of gas increases linearly with the absolute temperature. This rises more rapidly than the velocity of sound so, all other things being equal, the higher the gas temperature the longer it will take to expel the charge.
Although of much less importance in the flow regime (Reynolds number) in an exhaust, the viscosity of gasses increases with temperature - quite the reverse of the behaviour of liquids! - and this will very slightly inhibit the exhaust.
Another way of looking at the problem is via Bernoulli's equation which is appropriate for subsonic flow.
Pressure = 0.5 density x speed squared.
Now if we increase the temperature of the gasses flowing down a given pipe we reduce the density (inversely as the absolute temperature). However, if the mass of gas flowing per second is kept constant the speed must increase to keep density x speed the same. If we plug this back into Bernoulli's equation we see that the pressure needed to drive this flow has increased linearly with speed.
Edited by - Colin Mill on 10 Jun 2008 08:58:56