A compressed air tank contains 5 kg of air at a temperature of 80^∘ C . A gage on the tank reads

step 1 So in this question what we are given is that there is a compressed air tank right that contains

A compressed air tank contains 5 kg of air at a temperature...

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Key Concepts

Gauge vs Absolute Pressure

In many practical situations, pressure is measured as gauge pressure, which represents the pressure above atmospheric pressure. When using the ideal gas law, it is essential to convert gauge pressure to absolute pressure by adding the atmospheric pressure, ensuring the calculations reflect the true thermodynamic state of the gas.

Mass-Based Gas Calculations

When calculations involve the mass of a gas instead of the number of moles, it is necessary to convert the mass to moles using the gas's molecular weight or apply a specific gas constant tailored to the gas. This approach permits the use of the ideal gas law to find unknown properties like volume.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental principle in thermodynamics that relates the pressure, volume, temperature, and number of moles (or mass) of a gas. It is used to solve various problems involving gas behavior under changing conditions, provided the gas behaves ideally.

Temperature Conversion

Thermodynamic calculations require the temperature to be in Kelvin rather than Celsius or Fahrenheit, because the Kelvin scale is an absolute temperature scale. This conversion ensures that the mathematical relationships in the ideal gas law are applied correctly.

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