The volume V of a given mass of a gas varies directly as the...

The volume $V$ of a given mass of a gas varies directly as the temperature $T$ and inversely as the pressure $P .$ If $V=231 \mathrm{cm}^{3}$ when $T=300^{\circ} \mathrm{K}$ (Kelvin) and $P=20 \mathrm{lb} / \mathrm{cm}^{2},$ what is the volume when $T=320^{\circ} \mathrm{K}$ and $P=16 \mathrm{Ib} / \mathrm{cm}^{2} ?$

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Key Concepts

Direct Variation

This concept describes a relationship in which one variable increases or decreases in direct proportion to another. In a direct variation, as one variable increases, the other increases at a constant rate, and the relationship can be expressed with an equation of the form y = kx, where k is the constant of proportionality.

Inverse Variation

This concept describes a relationship where one variable increases as the other decreases at a constant rate. In an inverse variation, the product of the two variables remains constant, and the relationship can be written as y = k/x, where k is the constant of proportionality used to maintain the balance between the variables.

Constant of Proportionality

The constant of proportionality is the fixed number that relates two variables in direct or inverse variation. It serves as the scaling factor in the equations representing proportional relationships, ensuring that the relationship remains consistent regardless of the specific values of the variables.

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