Solve each problem. Volume of a Gas Natural gas provides 25...

Solve each problem. Volume of a Gas Natural gas provides $25 \%$ of U.S. energy. The volume of a gas varies inversely with the pressure and directly with the temperature. (Temperature must be measured in degrees Kelvin (K), a unit of measurement used in physics.) If a certain gas occupies a volume of 1.3 liters at $300 \mathrm{K}$ and a pressure of 18 newtons per square centimeter, find the volume at $340 \mathrm{K}$ and a pressure of 24 newtons per square centimeter.

Solve each problem.
Volume of a Gas Natural gas provides $25 \%$ of U.S. energy. The volume of a gas varies inversely with the pressure and directly with the temperature. (Temperature must be measured in degrees Kelvin (K), a unit of measurement used in physics.) If a certain gas occupies a volume of 1.3 liters at $300 \mathrm{K}$ and a pressure of 18 newtons per square centimeter, find the volume at $340 \mathrm{K}$ and a pressure of 24 newtons per square centimeter.

Key Concepts

Kelvin Temperature Scale

The Kelvin temperature scale is an absolute temperature scale used in scientific measurements, particularly in gas law problems. Unlike degrees Celsius or Fahrenheit, Kelvin starts at absolute zero, making it essential for accurately relating temperature to gas volume in physics.

Constant of Proportionality

The constant of proportionality is a fixed value that relates the varying quantities in a direct or inverse variation relationship. In combined variation problems, this constant is determined using known values and is critical for calculating unknown quantities.

Direct Variation

Direct variation describes a relationship where one variable increases or decreases in direct proportion to another. In the given problem, the volume of the gas increases proportionally with the temperature, meaning if the temperature goes up, so does the volume, provided that other factors remain constant.

Inverse Variation

Inverse variation describes a relationship where one variable increases as the other decreases. In the context of this problem, the volume of the gas decreases as the pressure increases, indicating that the two are inversely related.

Combined Variation

Combined variation occurs when a variable is simultaneously varying directly with one or more variables and inversely with others. For the gas problem, the volume is directly proportional to the absolute temperature and inversely proportional to the pressure, integrating both types of variation into one relationship.

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