Question

Two identical rooms in a house are connected by an open doorway. The temperatures in the two rooms are maintained at different values. Which room contains more air?
A. The room with higher temperature
B. The room with lower temperature
C. The room with higher pressure
D. Same, as both have the same pressure and volume

Answer 1

Understand the given situation carefully. It is mentioned in the question that the rooms are identical so the volume of the rooms should be the same. Now we could recall the ideal gas equation and thus find the relation between the pressure and temperature with the amount of substance.

Formula used:
Ideal gas equation, $PV=nRT$

Complete answer:
In the question, we are given two identical rooms that are connected by an open doorway. We are also told that the temperatures in these two rooms are maintained at different values.Under these given conditions, we have to find which of the given rooms contains more air.
Now let us recall the ideal gas equation in order to answer this question.
This equation is more of the equation of state of a hypothetical ideal gas and is given by,
$PV=nRT$
Where, P is the pressure, V is the volume, T is the temperature, n is the amount of substance and R is the ideal gas constant. This relation is actually derived from the microscopic kinetic theory.
From the ideal gas equation we see that the amount of substance (n) is directly proportional to the pressure and volume and is inversely proportional to the temperature of the substance. We are given that the rooms are identical, so the volume of the rooms will be the same.
As the temperature is different for both rooms, from the ideal gas equation we know that the amount of air contained will be lower for the room that is at higher temperature and higher in the room that is at lower temperature. So, we find that option B is true.
Also, the amount of air will be more for the room at higher pressure and lower for the room with lower pressure. So, option C is also true.

Hence, we found that options B and C are the correct options.

Note:
You may wonder why we have used the ideal gas equation when there is no mention of ideal gas in the question. This equation could also be applied for real gases that can sufficiently behave like an ideal gas. The universal gas constant R can be given by the product of Boltzmann constant and the Avogadro constant.