Consider two different containers, each filled with 2 moles of \(\mathrm{Ne}(g)\) . One of the containers is rigid and has constant volume. The other container is flexible (like a balloon) and is capable of changing its volume to keep the external pressure and internal pressure equal to each other. If you raise the temperature in both containers, what happens to the pressure and density of the gas inside each container? Assume a constant external pressure.

For the rigid container with a constant volume, the equation of state can be written as: \(P = \frac{nRT}{V}\) As we raise the temperature (T), it's clear from this equation that the pressure (P) will increase proportionally. Since the volume stays constant, the density of the gas will remain unchanged.

For the flexible container that can change its volume, we need to consider that the internal pressure and external pressure are equal. So, we can write the equation of state as: \(P_{ext} = \frac{nRT}{V}\) Since the external pressure (P_ext) remains constant, as we raise the temperature (T), the volume (V) needs to increase proportionally to keep the pressure constant. Therefore, the pressure inside the flexible container remains constant. Now let's consider the relationship between density, mass, and volume for the flexible container: \(\rho = \frac{m}{V}\) Since the mass (m) of the gas inside the container remains constant and the volume (V) increases, the density of the gas (ρ) will decrease as the temperature increases. To sum up, when the temperature is raised: - In the rigid container (constant volume): pressure increases and density remains unchanged. - In the flexible container (variable volume): pressure remains constant, and density decreases.