Gas Laws | Jamb(UTME)

Boyle’s Law (Isothermal Process)

1. Boyle’s Law states that the pressure of a fixed amount of gas is inversely proportional to its volume, provided the temperature remains constant.
2. Mathematically, $P \propto \frac{1}{V}$ or $PV = \text{constant}$.
3. The formula for Boyle’s Law is:
   
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   $P_1 V_1 = P_2 V_2$
4. If the volume of a gas decreases, its pressure increases, assuming constant temperature.
5. This law describes isothermal processes, where the temperature remains unchanged.
6. Boyle’s Law is observed when compressing a gas in a syringe—the pressure increases as the volume decreases.
7. It is crucial in understanding the behavior of gases in closed systems, such as scuba diving tanks.
8. The graph of $P$ versus $V$ is a hyperbola, while $P$ versus $\frac{1}{V}$ is a straight line.
9. Boyle’s Law explains why atmospheric pressure decreases at higher altitudes due to the expansion of gases.
10. The law assumes the gas behaves ideally, with no intermolecular forces.
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Charles’s Law (Isobaric Process)

11. Charles’s Law states that the volume of a fixed amount of gas is directly proportional to its temperature, provided the pressure remains constant.
12. Mathematically, $V \propto T$ or $\frac{V}{T} = constant$.
13. The formula for Charles’s Law is:
    
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    $\frac{V_1}{T_1} = \frac{V_2}{T_2}$
14. If the temperature of a gas increases, its volume also increases, assuming constant pressure.
15. This law describes isobaric processes, where pressure remains constant.
16. The temperature used must be in Kelvin for accurate calculations.
17. Charles’s Law explains why hot air balloons rise—heated air expands, decreasing its density.
18. The graph of $V$ versus $T$ is a straight line passing through the origin.
19. The law is applied in designing expandable materials that respond to temperature changes.
20. It assumes the gas behaves ideally without interactions between molecules.
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Pressure Law (Volumetric Process)

21. The Pressure Law states that the pressure of a fixed amount of gas is directly proportional to its temperature, provided the volume remains constant.
22. Mathematically, $P \propto T$ or $\frac{P}{T} = constant$.
23. The formula for the Pressure Law is:
    
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    $\frac{P_1}{T_1} = \frac{P_2}{T_2}$
24. If the temperature of a gas increases, its pressure also increases, assuming constant volume.
25. This law describes isochoric processes, where volume remains constant.
26. Pressure law explains why sealed containers may burst when heated—gas pressure increases.
27. Temperature must be in Kelvin for calculations using the Pressure Law.
28. The graph of $P$ versus $T$ is a straight line passing through the origin.
29. The Pressure Law is crucial in safety designs for pressure vessels and gas storage.
30. It assumes the gas behaves ideally under given conditions.
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Absolute Zero of Temperature

31. Absolute zero is the lowest possible temperature, at which a gas would have zero volume and pressure.
32. It is defined as $0 K$ or $-273.15^\circ C$.
33. At absolute zero, molecular motion theoretically stops, meaning particles have no kinetic energy.
34. Absolute zero is the starting point of the Kelvin temperature scale.
35. It is unattainable in practice but serves as a reference point for thermodynamic calculations.
36. Absolute zero is inferred from extrapolating Charles’s and the Pressure Law graphs to zero volume or pressure.
37. It helps define the third law of thermodynamics.
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General Gas Equation

38. The general gas equation combines Boyle’s Law, Charles’s Law, and the Pressure Law.
39. The equation is:
    
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    $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$
40. It relates pressure, volume, and temperature for a fixed amount of gas.
41. The equation assumes the gas behaves ideally.
42. It is used in calculations involving changes in multiple variables of a gas system.
43. The general gas equation simplifies to specific laws if one variable remains constant e.g., $V$, $T$, or $P$.
44. All temperatures must be converted to Kelvin before using the equation.
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Ideal Gas Equation

45. The ideal gas equation describes the behavior of an ideal gas under all conditions.
46. The equation is:
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    $PV = nRT$ where:
    • $P$ = Pressure,
    • $V$ = Volume,
    • $n$ = Number of moles,
    • $R$ = Universal gas constant $(8.314J/mol·K)$,
    • $T$ = Temperature in Kelvin.
47. The ideal gas equation combines the general gas equation and Avogadro’s law.
48. It applies to gases that follow the assumptions of ideal gas behavior.
49. The ideal gas equation is widely used in physics, chemistry, and engineering.
50. It provides a framework for understanding gas behavior under different conditions.
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Van der Waals Gas

51. Real gases deviate from ideal gas behavior at high pressures and low temperatures.
52. The Van der Waals equation accounts for intermolecular forces and finite molecular sizes.
53. The equation is:
    
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    $\left( P + \frac{a}{V^2} \right) \left( V - b \right) = RT$ where:
    • $a$ accounts for intermolecular attractions,
    • $b$ corrects for the finite size of gas molecules.
54. $a$ and $b$ are specific to each gas and depend on its properties.
55. The Van der Waals equation reduces to the ideal gas equation when $a$ and $b$ are negligible.
56. It explains why gases condense into liquids at high pressures or low temperatures.
57. Van der Waals gas behavior is important in studying phase transitions and critical points.
58. The equation is used in designing compressors, liquefied gas systems, and refrigeration.
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Applications and Practical Considerations

59. Boyle’s Law is used in syringes, hydraulic systems, and scuba diving equipment.
60. Charles’s Law is applied in hot-air balloons and temperature compensation systems.
61. The Pressure Law is critical in designing pressure vessels and gas safety devices.
62. The general gas equation explains weather balloon behavior at varying altitudes.
63. The ideal gas equation is used in calculating gas flow rates and energy transfers.
64. Absolute zero serves as a benchmark for low-temperature physics experiments.
65. Van der Waals theory bridges the gap between ideal and real gas behavior.
66. Gas laws are used in HVAC (heating, ventilation, and air conditioning) systems.
67. The behavior of gases under changing conditions is crucial in aviation and space exploration.
68. Understanding deviations from ideal gas laws helps improve gas storage and transportation systems.
69. Gas laws form the foundation of thermodynamics and statistical mechanics.
70. Accurate gas behavior predictions are essential in industrial processes and environmental studies.
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