Exploring the Pressure Change in a Syringe: Understanding Boyle's Law and Isothermal Processes

When conducting a simple experiment with a syringe containing air, you might ask, A syringe of air has its end sealed at volume 5 cm3 and is then pulled out to 10 cm3. What is the new resultant pressure inside the syringe? This question delves into the principles of pressure, volume, and temperature in gases, particularly through the use of Boyle's Law and isothermal processes.

Boyle's Law and Isobaric Processes

Boyle's Law states that for a fixed amount of a gas at constant temperature, pressure (P) is inversely proportional to volume (V). Mathematically, this is represented as:

PV constant

In the scenario where the end of the syringe is sealed, the number of moles of gas (N) and the temperature (T) are constant. Thus, we can use Boyle's Law to calculate the new pressure when the volume changes.

Applying Boyle's Law

Let's consider the initial and final states of the syringe:

Initial State:

Pressure (P1) 1 atm

Volume (V1) 5 cm3

Resultant State:

Volume (V2) 10 cm3

Pressure (P2) ?

Using Boyle's Law, we can express the relationship as:

P1V1 P2V2

Substituting the known values:

1 atm × 5 cm3 P2 × 10 cm3

Solving for P2:

P2 (1 atm × 5 cm3) / 10 cm3 0.5 atm

Therefore, the new resultant pressure inside the syringe is 0.5 atm.

Isothermal Processes and Temperature Effects

While Boyle's Law provides a straightforward solution in isobaric processes, real-world scenarios often involve more complex thermodynamic processes. When the volume of a gas is changed without allowing heat exchange with the surroundings, the temperature of the gas changes as well.

Isentropic Expansion

Isentropic expansion is a process where a gas is allowed to expand adiabatically (without heat exchange with the surroundings) and the temperature decreases. In such a case, you would need to use the adiabatic equation of state, which is different from Boyle's Law:

PVγ constant (where γ is the adiabatic index)

This equation accounts for the pressure-temperature relationship during expansion, where both pressure and temperature change.

In isothermal processes, where the temperature remains constant, the system can exchange heat with the surroundings, allowing the pressure to be calculated directly using Boyle's Law. This is the reason pressure decreases when a gas expands isothermally, as the volume increases.

Practical Application and Experimentation

Understanding the theoretical principles is one thing, but observing these principles in practice is another. Consider a school demonstration where carbon dioxide from a cylinder is rapidly expanded into a vacuum. The rapid expansion causes the gas to cool and condense into dry ice (solid carbon dioxide). This experiment not only illustrates Boyle's Law but also highlights the importance of temperature changes during different types of gas expansions.

Similarly, using a CO2 fire extinguisher requires caution due to the sudden release of gas, causing a temporary drop in temperature and increasing the risk of frostbite. This underscores the practical importance of understanding the behavior of gases under different conditions.

Conclusion

The pressure change in a syringe when the volume is increased can be calculated using Boyle's Law if the process is isothermal. However, in real-world scenarios, the process might not be strictly isothermal, and other factors such as adiabatic expansion come into play. Understanding these principles is crucial for students and professionals alike, as it provides a solid foundation for more advanced thermodynamic studies.

Related Keywords

Boyle's Law: Understanding the inverse relationship between pressure and volume for a fixed amount of gas at a constant temperature.

Pressure Change in Syringe: An application of thermodynamic principles to everyday objects.

Isothermal Process: A detailed explanation of how the temperature remains constant during volume changes in a gas.