A helium-filled toy balloon has a gauge pressure of 0.200...

Name: Problem 11, Chapter 15: College Physics
Uploaded: 2019-10-08T03:57:03-08:00
Duration: 3 min 9 s
Channel: Charles Magnusen
Description: A helium-filled toy balloon has a gauge pressure of 0.200 atm and a volume of 10.0 L. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?

A helium-filled toy balloon has a gauge pressure of 0.200 atm and a volume of 10.0 L. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?

Key Concepts

Gauge Pressure

Gauge pressure is defined as the pressure measured relative to the ambient atmospheric pressure. It shows by how much the internal pressure of a system (such as a balloon) exceeds or is below the surrounding atmospheric pressure. Recognizing the difference between gauge and absolute pressure is important in thermodynamics because many formulas use absolute pressure, so converting gauge pressure to absolute pressure is often a necessary step in calculations.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates pressure (P), volume (V), temperature (T), and the amount of gas in moles (n) through the universal gas constant (R). This law is essential when analyzing the behavior of gases under conditions where they act ideally, and it allows us to connect changes in pressure or volume to changes in other state parameters, such as internal energy.

Internal Energy of a Monatomic Ideal Gas

For a monatomic ideal gas, such as helium, the internal energy is determined solely by its temperature and is given by U = (3/2) nRT. When applying the ideal gas law, this expression can also be written in terms of pressure and volume as U = (3/2) P V, assuming constant temperature. Understanding this relationship clarifies how changes in pressure (or volume) for a gas at a fixed temperature can reflect changes in its total internal energy.

Unit Conversion in Thermodynamics

Unit conversion is a key aspect in thermodynamic calculations, especially when pressures and volumes are used to compute energy. For example, converting atm·L to Joules (with 1 atm·L equaling approximately 101.325 Joules) is often necessary to ensure that the final results are presented in the appropriate SI units. This step is vital for accurately comparing energy values in different systems or against standard energy units.

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