Understanding the Impact of Temperature on Gas Pressure

The Ideal Gas Law, represented by the formula PV = nRT, describes the relationship between pressure (P), volume (V), number of moles (n), the gas constant (R), and temperature (T) of an ideal gas. In a closed system, when the volume remains constant, changes in temperature directly affect the pressure.

Example 1: Heating a Sealed Container

Scenario:

Consider a sealed container with a volume of 2.0 liters filled with a gas at an initial temperature of 20°C (293 K) and an initial pressure of 1.0 atm. We want to investigate what happens when we increase the temperature to 80°C (353 K).

Calculation:

Using the Ideal Gas Law, we can rearrange the formula to find the new pressure:

1. Initial Conditions:

   • V = 2.0 L
   • T₁ = 293 K
   • P₁ = 1.0 atm

2. Final Conditions:

   • T₂ = 353 K
   • V = 2.0 L (constant)

3. Using the formula:

   Since volume is constant, we can use the relationship:

   \\( \frac{P_1}{T_1} = \frac{P_2}{T_2} \)

   Rearranging gives us:
   \\( P_2 = P_1 \times \frac{T_2}{T_1} \)

4. Plugging in the values:
   \\( P_2 = 1.0 \times \frac{353}{293} \)
   \\( P_2 ≈ 1.20 \, atm \)

Conclusion:

As the temperature increased from 20°C to 80°C, the pressure in the container rose from 1.0 atm to approximately 1.20 atm, demonstrating the direct relationship between temperature and pressure in a closed system.

Example 2: Cooling a Gas in a Balloon

Scenario:

Imagine a balloon filled with air at an initial temperature of 30°C (303 K) and a pressure of 1.5 atm. We then place this balloon in a refrigerator, lowering the temperature to 10°C (283 K).

Calculation:

1. Initial Conditions:

   • V = constant (the balloon expands or contracts)
   • T₁ = 303 K
   • P₁ = 1.5 atm

2. Final Conditions:

   • T₂ = 283 K

3. Using the formula:
   \\( P_2 = P_1 \times \frac{T_2}{T_1} \)

4. Plugging in the values:
   \\( P_2 = 1.5 \times \frac{283}{303} \)
   \\( P_2 ≈ 1.40 \, atm \)

Conclusion:

When the temperature decreased from 30°C to 10°C, the pressure inside the balloon dropped from 1.5 atm to approximately 1.40 atm. This further confirms that lowering the temperature in a closed system results in a decrease in gas pressure.

Summary

These examples illustrate the fundamental relationship governed by the Ideal Gas Law: as temperature increases in a closed system, pressure increases, and conversely, as temperature decreases, pressure decreases. Understanding this relationship is crucial for various applications in chemistry, physics, and engineering.