Suppose you have a container of gas and you can somehow run time at 2x speed in that container. It would be obvious that from an external observer’s point of view (where time is running at 1x speed) that sound would appear to travel 2x as fast from one end of the container to the other. But to the external observer, running time at 2x speed is indistinguishable from doubling the velocity of each gas molecule at 1x speed. So increasing the velocity of molecules (and therefore the temperature) should cause sound to travel faster.
(Also, for more questions like this, see this post on Thinking Physics)
This seems like it should work at first glance, but doesn’t. The initial intervention (double particle speed, which quadruples total kinetic energy) at first doubles pressure (each particle imparts twice as much force when it hits a wall and reverses direction), but the velocity distribution is no longer thermal. In a statistical mechanics sense, you’ve added energy without adding any entropy, and that means the colloquial concept of temperature for a gas doesn’t really apply, just like accelerating a car by applying macroscopic kinetic energy doesn’t mean you increased it’s temperature (but over time, friction will thermalize the kinetic energy). After that initial transformation, I think the gas will thermalize over a fairly short time but I’m not 100% sure. If it does, then in that case you’ve quadrupled total internal energy (1.5nRT or PV for a monatomic ideal gas), so I think it should stabilize at quadruple the T and P. Which, yes, will double v(sound), but doesn’t tell you whether that’s because of the T or the P or both. In any case this transformation put the system in an unnaturally low-entropy state, and so a lot of the usual assumptions about ideal gas behavior won’t apply.
Here’s a handwavy attempt from another angle:
Suppose you have a container of gas and you can somehow run time at 2x speed in that container. It would be obvious that from an external observer’s point of view (where time is running at 1x speed) that sound would appear to travel 2x as fast from one end of the container to the other. But to the external observer, running time at 2x speed is indistinguishable from doubling the velocity of each gas molecule at 1x speed. So increasing the velocity of molecules (and therefore the temperature) should cause sound to travel faster.
(Also, for more questions like this, see this post on Thinking Physics)
This seems like it should work at first glance, but doesn’t. The initial intervention (double particle speed, which quadruples total kinetic energy) at first doubles pressure (each particle imparts twice as much force when it hits a wall and reverses direction), but the velocity distribution is no longer thermal. In a statistical mechanics sense, you’ve added energy without adding any entropy, and that means the colloquial concept of temperature for a gas doesn’t really apply, just like accelerating a car by applying macroscopic kinetic energy doesn’t mean you increased it’s temperature (but over time, friction will thermalize the kinetic energy). After that initial transformation, I think the gas will thermalize over a fairly short time but I’m not 100% sure. If it does, then in that case you’ve quadrupled total internal energy (1.5nRT or PV for a monatomic ideal gas), so I think it should stabilize at quadruple the T and P. Which, yes, will double v(sound), but doesn’t tell you whether that’s because of the T or the P or both. In any case this transformation put the system in an unnaturally low-entropy state, and so a lot of the usual assumptions about ideal gas behavior won’t apply.
Interesting, thanks for the detailed responses here and above!