Pressure-Temperature Relationships

Introduction to Galu Saxe Law

• Galu Saxe Law: Relationship between pressure and temperature for a fixed amount of an ideal gas at constant volume.

Concepts and Demonstration

• A candle is lit in a beaker filled with colored water to visualize air pressure changes.
• Combustion requires oxygen from the air, and burning the candle reduces the oxygen inside the beaker.
• As oxygen burns, the temperature rises due to the heat from the candle.
• When the flame extinguishes, the temperature drops, leading to fewer collisions and lower pressure inside the beaker.
• Atmospheric pressure then pushes the water upward into the beaker due to the pressure differential.

Key Points of Galu Saxe Law

• The law states: $\frac{P<em>1}{T</em>1} = \frac{P<em>2}{T</em>2}$
  • Where:
  • $P$: Pressure
  • $T$: Temperature
• Direct relationship:
  • Increasing temperature increases kinetic energy, leading to more collisions with container walls, thus increasing pressure.
  • If pressure goes up, temperature must also rise, confirming their direct relationship.

Examples

Example 1: Pressure Cooker Calculation

• Initial conditions:
  • $P_1 = 1 ext{ ATM}$
  • $T_1 = 22^{\circ}C = 295 ext{ K}$
• Final temperature:
  • $T_2 = 150^{\circ}C = 423 ext{ K}$
• Using the equation:
  • $\frac{P<em>1}{T</em>1} = \frac{P<em>2}{T</em>2}$
• Solve for $P_2$:
  • $P<em>2 = \frac{P</em>1 \cdot T<em>2}{T</em>1}$
  • $P_2 = \frac{1 ext{ ATM} \cdot 423 ext{ K}}{295 ext{ K}} = 1.43 ext{ ATM}$
• Interpretation: The pressure rises with increasing temperature, validating the law.

Example 2: Gas Sample Calculation

• Initial conditions:
  • $P_1 = 45 ext{ kPa}$
  • $T_1 = 274 ext{ K}$
• Final pressure desired:
  • $P_2 = 25 ext{ kPa}$
• Use the formula:
  • $\frac{P<em>1}{T</em>1} = \frac{P<em>2}{T</em>2}$
• Rearranging gives:
  • $T<em>2 = \frac{P</em>2 \cdot T<em>1}{P</em>1}$
  • Plugging in gives:
  • $T_2 = \frac{25 ext{ kPa} \cdot 274 ext{ K}}{45 ext{ kPa}} = 152 ext{ K}$
• Change in temperature:
  • $\Delta T = T<em>2 - T</em>1 = 152 ext{ K} - 274 ext{ K} = -122 ext{ K}$
• Conclusion: A decrease in temperature shows how pressure and temperature are inversely related in gas behavior.

Conclusion

• Galu Saxe Law illustrates the fundamental principles governing gas behavior under varying temperature and pressure. Understanding these relationships is critical in various scientific applications, including pressure cookers, combustion engines, and atmospheric science.