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Chapter 5: Problem 26

Consider two different containers, each filled with 2 moles of \(\mathrm{Ne}(\mathrm{g})\). 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.

Short Answer

Expert verified
In the rigid container with constant volume, when the temperature increases, the pressure increases and the density remains constant. In the flexible container with variable volume under constant external pressure, when the temperature increases, the pressure remains constant and the density decreases.

Step by step solution

01

Analyze the rigid container with constant volume

For the first container with a constant volume, the internal volume will remain the same as we increase the temperature. Therefore, our main focus is to determine the effect on pressure and density.
02

Determine the effect on pressure for the rigid container

Using the Ideal Gas Law equation for the first container: PV = nRT Since the volume V and the number of moles n are constant, we can rewrite the equation as: P = nRT/V When the temperature T increases, since n, R, and V are constant, the pressure P will also increase. Thus, the pressure inside the rigid container increases as the temperature increases.
03

Determine the effect on density for the rigid container

Density (ρ) is given by: ρ = n/V Since both the number of moles n and the volume V are constants, the density ρ remains constant as temperature increases. Therefore, the density of the gas inside the rigid container does not change when the temperature increases.
04

Analyze the flexible container with variable volume

For the second container, the volume can change to keep the internal pressure equal to the external pressure, which is constant. Thus, our main focus is to determine the effect on volume and density.
05

Determine the effect on volume for the flexible container at constant pressure

Since the pressure inside the container is equal to the constant external pressure, as temperature increases, the volume will also increase in order to maintain the constant pressure using the Ideal Gas Law equation: PV = nRT Since P is constant, we can rewrite the equation as: V = nRT/P As temperature T increases, since n, R, and P are constant, the volume V will also increase. Thus, the volume of the container increases as the temperature increases.
06

Determine the effect on density for the flexible container

Density (ρ) is given by: ρ = n/V As the volume V increases due to the increase in temperature (from Step-5), the density ρ will decrease. Therefore, the density of the gas inside the flexible container decreases as the temperature increases. In conclusion: - In the rigid container with constant volume, as temperature increases, the pressure increases while the density remains constant. - In the flexible container with variable volume, as temperature increases, the pressure remains constant while the density decreases.

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