Question

Consider two equal size rooms connected by an open door. One room is maintained at a higher temperature then the other one. Which room contains more air molecules? Explain.

Answer 1

Answer:

• The room mantained at a lower temperature will contain more air molecules.

Explanation:

1) Since the two rooms are connected by an open door, you assume pressure equilibrium: the pressure on the two rooms is the same.

2) Since you consider two equal size rooms, both volumes are equal.

3) Assuming ideal gas behavior, pressure (P), temperature (T), volume (V) and number of moles (n) are related by the equation PV = nRT

4) Naming T₁ the lower temperature, T₂ the higher temperature, n₁ the number of moles of air in the room at lower temperature, and n₂ the number of moles of air in the room at higher temperature, you get:

• n₁ T₁  = n₂ T₂, or n₁ / n₂ = T₂ / T₁

5) That means that the amount of molecules (number of moles) is inversely related to the temperature: the higher the temperature the lower the number of moles, and the lower the temperature the greater the number of moles.

Hence, the answer is that the room that contains more air molecules is the room mantained at a lower temperature.