Question

Suppose that you are studying kinetic energy of helium molecules: A helium weather balloon rises to an altitude of \(40,000 \mathrm{ft} ;\) the temperature of the gas drops to \(-70{ }^{\circ} \mathrm{F}\). (a) Make an appropriate choice of system and surroundings and describe it unambiguously. (b) Explain why you chose the system and surroundings you did. (c) Identify transfers of energy and material into and out of the system that would be important for you to monitor in your study.

Short answer

System: Helium gas in the balloon. Monitor thermal energy exchanges with surroundings.

Step-by-step solution

Define the System

In thermodynamics, a system is a specific portion of matter chosen for study, while the surroundings are everything else. In this case, we choose the helium gas inside the weather balloon as the system. This allows us to focus on the kinetic energy of helium molecules.

Define the Surroundings

The surroundings include everything outside the weather balloon. This consists of the atmosphere at the altitude of 40,000 feet, any sunlight, air currents, and other environmental factors that could interact with the balloon.

Justify System Choice

The helium gas inside the balloon is chosen as the system because the problem focuses on studying its kinetic energy, which depends on the temperature and movement of these molecules. By isolating this portion, we can more effectively monitor and analyze the changes in kinetic energy specifically.

Identify Energy Transfers

Important energy transfers include thermal energy exchanged between the helium and the surrounding atmosphere. The balloon will likely cool as it rises due to the lower temperature at the higher altitude.

Material Transfers

In typical balloon operation, we assume no helium enters or leaves the balloon, so material transfer is not something to monitor in this study. However, leakage through the balloon's material may need consideration if the study shows discrepancies.

Key concepts

Thermodynamic Systems

In thermodynamics, the concept of a system is essential for analyzing energy changes. A system refers to the specific portion of matter or space that is selected for study. Everything outside of this system is considered the surroundings. By defining these boundaries, scientists can better understand how systems interact with their environments. The system we choose is crucial because it helps us isolate the processes and measure changes effectively.

In the exercise involving a helium weather balloon, the helium gas inside the balloon is chosen as the system. This choice is deliberate because our goal is to study the kinetic energy of the helium molecules. Kinetic energy is influenced by temperature and the movement of molecules. Therefore, by focusing on the helium, you're looking directly at the factors influencing kinetic energy without interference from other variables.

• The system is the helium gas in the balloon.
• The surroundings are the atmosphere and environmental factors.

The selection of a system allows for a controlled analysis of energy interaction, necessary for uncovering detailed thermodynamic insights.

Energy Transfer

Energy transfer in thermodynamic systems involves the movement of energy across the system boundary. This movement can occur through various forms, such as thermal, mechanical, or electrical energy. For the helium balloon scenario, thermal energy transfer is of significant interest. As the balloon ascends, the external temperature at 40,000 feet is much lower, affecting the kinetic energy of the helium molecules.

Key energy transfer considerations for this system include:

• Thermal Energy: As the balloon rises, the kinetic energy of the helium gas changes due to exposure to colder air. Monitoring this thermal exchange is crucial for understanding how the gas behaves at different altitudes.
• Potential Energy: Though not directly linked to kinetic energy, the change in altitude may affect potential energy indirectly affecting the setup of the weather balloon itself.

Understanding these energy flows helps predict how the helium's kinetic energy might reduce, potentially bringing it to a thermal equilibrium with the colder surroundings.

Chemical Thermodynamics

Chemical thermodynamics extends the basic thermodynamic principles to chemical reactions and processes. In the context of a helium weather balloon, it may seem less obvious, but understanding chemical thermodynamics can still be relevant. Chemical thermodynamics provides insights into how the physical state of a system changes with energy transfer, even though no chemical reactions are primarily occurring with helium.

One element to consider is the ideal gas law, which relates temperature, pressure, and volume. As the balloon rises, the external pressure decreases, which may affect the volume and pressure of the helium gas:

• Pressure Changes: Higher altitudes have lower pressures. This could cue changes in volume if the balloon material allows for expansion.
• Temperature's Role: As temperature drops, it affects the gas's pressure and volume, indirectly influencing kinetic energy.

By understanding these principles, one can predict and comprehend how energy is transferred and how it affects the physical properties of the helium, ensuring a more accurate study of its behavior under different atmospheric conditions.