The density of an ideal gas is inversely proportional to its absolute temperature.
Density, pressure, and temperature are related within the ideal gas law, leading to this inverse relationship when pressure is held constant. Let's explore this further:
Understanding the Relationship
The ideal gas law is expressed as:
PV = nRT
Where:
- P = Pressure
- V = Volume
- n = Number of moles
- R = Ideal gas constant
- T = Absolute temperature
Density (d) is defined as mass (m) per unit volume (V): d = m/V
We can rewrite the ideal gas law to include density:
- n = m/M, where M is the molar mass of the gas. Substituting this into the ideal gas law:
PV = (m/M)RT - Rearranging to isolate density (d = m/V):
d = (PM)/(RT)
From this equation, we can clearly see that:
- Density (d) is directly proportional to Pressure (P).
- Density (d) is inversely proportional to Absolute Temperature (T).
Therefore, if the pressure remains constant, an increase in temperature will result in a decrease in density, and vice versa.
Example
Imagine heating a fixed amount of air in a container while keeping the pressure constant. As the temperature increases, the air expands (volume increases), and since the mass remains the same, the density decreases.
Summary
In conclusion, the density of an ideal gas is inversely proportional to its absolute temperature, assuming the pressure remains constant.
