# terminal speed of the vessel

#### howard24

In vacuum and weightlessness, at the bottom of a cylindrical vessel (a cup), there is a layer of solid substance of molar mass μ. This substance sublimes slowly (evaporates from the solid phase into gaseous phase) and pushes thereby the vessel to the opposite direction. Estimate the terminal speed of the vessel. The mass of the vessel M, and the initial mass of the substance m ≪ M; the temperature of the vessel is T; the process can be assumed to be isothermal (cooling due to evaporation and heat radiation remains negligible). The
cross-sectional area of the vessel is A.

#### HallsofIvy

If this is "in vacuum and weightlessness" what do you mean by "up"? And why would a gas push the vessel "up"?

#### howard24

me neither understand that. but the answer should be:
V=m/M*sqrt(RT/miu) and I do not know how to get to it

#### oz93666

If this is "in vacuum and weightlessness" what do you mean by "up"? And why would a gas push the vessel "up"?
No where does the word "up " appear ..

The solid is in the base of the cup , subliming , that's to say atoms separate from the solid surface , become gas , the gas can only exit in one direction , the mouth of the cup ,the reaction pushes the cup the other direction.

The terminal speed must be dependent on the speed(temperature) of the gas molecules ... it must be the same as the velocity of gas molecules , because then the molecules cannot impact the surface imparting momentum , the surface is moving away as fast as they are travelling .

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#### Woody

Look at the momentum transfer
the momentum of the cup must be equal but opposite to the momentum of the gas molecules.

Also look at the ideal gas law.

#### oz93666

Look at the momentum transfer
the momentum of the cup must be equal but opposite to the momentum of the gas molecules.

Also look at the ideal gas law.
Unnecessary ...

All you need is the velocity of the gas molecules ...
that will be the terminal speed of the container
Because momentum will continue to be imparted to the container, increasing it's speed .. until it is moving away so fast gas molecules can no longer hit the surface sublimating.