A tank has two rooms separated by a membrane. Room A has 1 kg of air and a volume of 0.5 m^3 roo

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A tank has two rooms separated by a membrane. Room A has 1...

A tank has two rooms separated by a membrane. Room A has $1 \mathrm{kg}$ of air and a volume of $0.5 \mathrm{m}^{3}$ room $\mathrm{B}$ has $0.75 \mathrm{m}^{3}$ of air with density $0.8 \mathrm{kg} / \mathrm{m}^{3}$ The membrane is broken and the air comes to a uniform state. Find the final density of the air.

Key Concepts

Conservation of Mass

This principle states that within a closed system, the total mass remains constant regardless of the processes happening within the system. When two regions or substances are combined, the final total mass is simply the sum of the individual masses, as long as no mass is added or lost. This concept is fundamental in ensuring that calculations account correctly for the redistributed mass after mixing.

Density

Density is defined as the mass of a substance per unit volume. It is a key property in fluid mechanics and thermodynamics, used to describe how much mass is contained in a given volume. When different regions with varying densities mix, the final uniform density can be calculated by dividing the combined mass by the combined volume.

Volumetric Additivity

This concept involves treating the total volume of a system as the sum of the individual volumes when compartments or regions are merged. It is important that the volumes are added correctly in order to use them in further calculations, such as determining the overall density after the mixing process.

Thermodynamic Equilibrium

The concept of equilibrium in thermodynamics refers to the state where all parts of a system reach uniform properties, such as temperature, pressure, or density, following interaction or mixing. In this context, once the partition is removed, the air reaches a state where its density becomes uniform throughout the entire combined volume.

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