Problem 17 - An Introduction to Physical Science

Question

Choose the word or phrase that best answers the question. Which change results in an increase in gas pressure in a balloon? A) decrease in temperature B) decrease in volume C) increase in volume D) increase in altitude

Step-by-Step Solution

Answer

B) Decrease in volume

Step 1: Understanding Gas Pressure

Gas pressure is the force that the gas exerts on the walls of its container. It is influenced by factors such as temperature, volume, and the number of gas molecules.

Step 2: Consider Temperature

According to the ideal gas law (PV = nRTd), a decrease in temperature would result in a decrease in pressure if volume and the number of gas molecules remain constant. Thus, option A does not increase gas pressure.

Step 3: Analyze Volume

The ideal gas law also indicates that pressure and volume are inversely proportional (Boyle's Law: P1V1 = P2V2). Therefore, a decrease in volume results in an increase in pressure, making option B a potential correct answer.

Step 4: Review Increase in Volume

An increase in volume would decrease gas pressure, based on the same inverse relationship (Boyle’s Law). Hence, option C cannot be correct.

Step 5: Evaluate Altitude Effects

Increasing altitude reduces the atmospheric pressure outside the balloon, but it does not directly increase the internal gas pressure. Therefore, option D is not correct.

Step 6: Conclusion

After evaluating each option, it is clear that decreasing the volume (option B) is the change that results in an increase in gas pressure inside a balloon.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle that connects pressure, volume, temperature, and the number of moles of gas. It is expressed as \(PV = nRT\). Here:

• \(P\) is the pressure of the gas
• \(V\) is the volume
• \(n\) is the number of moles
• \(R\) is the ideal gas constant
• \(T\) is the temperature in Kelvin

This law tells us how these factors are related. For example, if you hold the volume and the number of moles constant, increasing the temperature will increase the pressure. Conversely, if the temperature decreases, the pressure decreases, provided the gas volume remains unchanged.

Boyle's Law

Boyle's Law describes the inverse relationship between pressure and volume for a fixed amount of gas at a constant temperature. Mathematically, it is expressed as \(P_1V_1 = P_2V_2\). This means if you decrease the volume of a gas, the pressure increases, and vice versa.
For example:

• If you have a gas at a volume of 2 liters and a pressure of 1 atmosphere, reducing the volume to 1 liter would double the pressure to 2 atmospheres, assuming the temperature remains constant.
• This is why option B is correct in the exercise, as decreasing the volume of the balloon increases the gas pressure inside it.

Temperature and Pressure Relationship

The relationship between temperature and pressure in a gas is a direct one. According to the Ideal Gas Law, if the volume is constant, increasing the temperature increases the pressure. This is because the gas molecules move faster at higher temperatures, colliding more frequently and forcefully with the container walls.
Consider a balloon:

• If you heat the balloon, the gas molecules inside move faster, increasing the internal pressure.
• This is why a decrease in temperature, as mentioned in the exercise’s step-by-step solution, would decrease the pressure if the volume and number of gas molecules remain the same.

Understanding these relationships is vital for predicting how gases will behave under different conditions, which is crucial in various scientific and practical applications.