Question

A cubic vessel (with faces horizontal $+$ vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of $500$ m/s in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground.

• A. Remains the same because $500$ m/s is very much smaller than $v_{rms}$ of the gas
• B. Remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls
• C. Will increase by a factor equal to $[v_{rms}^2+(500{)}^2]/v_{rms}^2$, where $v_{rms}$ was the original means square velocity of the gas
• D. Will be different on the top wall and bottom wall of the vessel

Answer 1

The correct option is B Remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls

As $P=\frac{nRT}{V}$, it (i.e., P) remains unaffected as n, R, T and V.

Here temperature of the vessel remain unchanged hence, the pressure remains same from that point of view.

now, let us discuss the phenomenon inside the vessel. the gas molecules keeps on colliding themselves as well as with the wall of containing vessel. these collision are perfectly elastic.

the number of collision per unit volume in the gas remains constant. so, the pressure inside the vessel remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules with respect to the walls.