Gases & Absolute Temperature

Absolute Temperature

• The Kelvin temperature scale commences at absolute zero.
  • At this point, 0 K corresponds to -273 °C.
  • A rise of 1 K equates to the same alteration as a rise of 1 °C.
• Temperatures below 0 K are unattainable, signifying that Kelvin temperatures cannot be negative.
• To convert between Celsius (θ) and Kelvin (T) scales, utilize the subsequent conversion:

The Gas Laws

If the temperature of a gas remains constant, changes in pressure occur when the gas is compressed or expanded:

• Compressed: Decreasing the volume increases the pressure.
• Expanded: Increasing the volume decreases the pressure.

• Likewise, alterations in pressure can induce variations in volume.
• A vacuum pump has the capability to extract air from a sealed enclosure.
• The illustration below illustrates how the volume of a inflated balloon alters when the surrounding air pressure diminishes:

• When gas is compressed, its molecules will collide with the container walls more often.
  • This results in a greater total force exerted on the walls, consequently raising the pressure.

Pressure & Temperature (Constant Volume)

• The velocity of molecules rises with temperature escalation, and diminishes when temperature decreases.
• Given that average kinetic energy is contingent on velocity, an increase in temperature, while keeping volume constant, also augments the kinetic energy of molecules.
  • Consequently, hotter gases exhibit higher average kinetic energy, whereas cooler ones manifest lower average kinetic energy.
• As gas heats up, its molecules accelerate, leading to more frequent collisions with container walls and consequent pressure escalation.
• Hence, at a constant volume, heightened temperature augments gas pressure, and conversely.
  • Diagram A illustrates how molecules in a fixed volume collide more frequently with container walls as temperature rises.
  • Diagram B portrays a linear graph since temperature and pressure are directly proportional.

Boyle's Law

• Boyle's Law describes the relationship between the pressure and volume of an ideal gas when the temperature remains constant.
  This means that as the pressure on a gas increases, its volume decreases, and vice versa.
• The relationship between pressure and volume for a fixed mass of gas at a constant temperature can be expressed as:
  P₁V₁ = P₂V₂
• Here, 
  • P₁ = initial pressure (Pa) 
  • P₂ = final pressure (Pa) 
  • V₁ = initial volume (m³) 
  • V₂ = final volume (m³)
• It's important to note that the units of volume are typically in cubic meters (m³) and pressure in Pascals (Pa).
  • Calculations involving different units, such as cm³ or MPa, can be directly converted as long as the final answer is given in the original units.