Temperature and Pressure Differences in Identical Rooms

[shrutiphysics]

Homework Statement

Two identical rooms in a perfectly insulated house are connected by an open doorway. The temperature in the two rooms are maintained at different values. The room which contains more air molecules is
(1) the one with the higher temperature
(2) the one with the lower temperature
(3) the one with the higher pressure
(4) neither, since both have the same volume

Homework Equations

i can't figure out? do i have to use gas laws like charles law or gay-lussac law?

The Attempt at a Solution

 

[CWatters]

Shouldn't really need to refer to any laws to answer this but you could if you wanted.

There are several parameters that describe a volume of gas...

Pressure
Volume
Temperature
Density
etc

Which are constant and which are variable or different in this particular set up?

 

[shrutiphysics]

Shouldn't really need to refer to any laws to answer this but you could if you wanted.

There are several parameters that describe a volume of gas...

Pressure
Volume
Temperature
Density
etc

Which are constant and which are variable or different in this particular set up?

if i take pressure as constant and use charles law then volume is directly proportional to temperature.so higher temperature more air molecules,
but the answer given is option b

 

[CWatters]

if i take pressure as constant and use charles law then volume is directly proportional to temperature.so higher temperature more air molecules, but the answer given is option b

The door is open so the pressure is the same/constant. That bit is correct,

Remind yourself how a hot air balloon works.

The bit about "higher temperature more air molecules" is incorrect.

 

[shrutiphysics]

The door is open so the pressure is the same/constant. That bit is correct,

Remind yourself how a hot air balloon works.

The bit about "higher temperature more air molecules" is incorrect.

is it like as hot air rise and hence the room with high temp has lower air molecules than the cooler one.
if it is right then maybe i have got it.

 

[CWatters]

Yes. Hot air is less dense than cold air (so hot air balloon rises).

Hot air is less dense because there are fewer molecules (less mass) per unit volume.

 

[CWatters]

Imagine if the rooms started at the same temperature (same number of molecules in each). Then you heat one room... The air in the hot room will expand and air molecules will push their way into the colder room until the pressure is the same again.

 

[shrutiphysics]

thanks for leading me to answer.