Is inertial mass of gas the same as its rest mass

[kahoomann]

Suppose we have a box at rest that is filled with a uniform gas. We denote the volume by V and the pressure by p. Suppose next that we apply a small force to the box and accelerate it until it has a speed v. The key question is: Is it harder to accelerate the gas because it takes work not only to accelerate the existing energy but also to compress the gas as the Lorentz contraction demands? In other words, is the inertia of the box is larger than just its rest mass?

 

[Mentz114]

This was discussed recently in this thread
https://www.physicsforums.com/showthread.php?t=213776

 

[Entropia]

The inertial mass of a gas is not the same as its rest mass. In classical mechanics, the inertial mass of an object is a measure of its resistance to acceleration, and is equal to its rest mass. However, in the context of special relativity, the concept of inertial mass becomes more complicated.

In special relativity, the rest mass of an object is the mass that it has when it is at rest. This mass is a fundamental property of the object and does not change with its velocity. On the other hand, the inertial mass of an object is a measure of its resistance to acceleration, and it can change depending on its velocity.

In the scenario described, when the box is at rest and filled with a uniform gas, the inertial mass of the box is equal to its rest mass. However, when the box is accelerated to a speed v, the inertial mass of the box increases due to the increased energy and momentum of the gas particles inside. This increase in inertial mass is a result of the Lorentz contraction, which compresses the gas in the direction of motion and requires additional work to be done to accelerate it.

In summary, the inertial mass of a gas is not the same as its rest mass, and it increases with velocity due to the effects of special relativity. Therefore, it is harder to accelerate the gas in the box because it not only requires work to accelerate the existing energy, but also to compress the gas as the Lorentz contraction demands.