A balloon behaves so the pressure is P=C2 V^1 / 3 C2=100 kPa / m . The balloon is blown up with

step 1 Here, the process is polytropic with component with exponent n is equal to minus 1 by 3. Here, p

A balloon behaves so the pressure is P=C2 V^1 / 3 C2=100 kPa...

A balloon behaves so the pressure is $P=C_{2} V^{1 / 3}$ $C_{2}=100 \mathrm{kPa} / \mathrm{m} .$ The balloon is blown up with air from a starting volume of $1 \mathrm{m}^{3}$ to a volume of $3 \mathrm{m}^{3} .$ Find the final mass of the air, assuming it is at $25^{\circ} \mathrm{C},$ and the work done by the air.

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Key Concepts

Ideal Gas Law

The Ideal Gas Law, expressed as PV = mRT or in other forms, relates the pressure, volume, temperature, and mass (or number of moles) of a gas. It is crucial for determining the state of the gas and for calculating quantities such as mass when pressure, volume, and temperature are known. In thermodynamic problems, this law provides the fundamental relationship needed to connect macroscopic observable properties of gases.

Pressure-Volume Work

Pressure-volume work refers to the work done by or on a gas when its volume changes, which is calculated by integrating the pressure with respect to the volume change (W = ? P dV). This concept is fundamental in thermodynamics where the process is not isobaric (constant pressure), and the integration takes into account how pressure varies as a function of volume.

Integration in Variable Pressure Processes

In many thermodynamic processes, the relationship between pressure and volume is not constant but follows a specific function. Evaluating the work in such cases involves integrating the given pressure function over the change in volume. This mathematical integration is essential to accurately determine the work done by or on the system, especially when the pressure-volume relationship is defined by a functional dependence rather than a constant value.

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