The balloon of Exercise 18 starts at 100 kPa pressure and rises to an altitude where p=75 kPa, m

The balloon of Exercise 18 starts at 100 kPa pressure and...

The balloon of Exercise 18 starts at $100 \mathrm{kPa}$ pressure and rises to an altitude where $p=75 \mathrm{kPa}$, maintaining a constant $300 \mathrm{~K}$ temperature. (a) By what factor does its volume increase? (b) How much work does the gas in the balloon do?

Key Concepts

Ideal Gas Law

This fundamental principle relates pressure, volume, temperature, and the number of moles of a gas through the equation pV = nRT. It allows one to deduce how one property of a gas will change if another property, such as pressure or temperature, is altered while keeping the other variables constant.

Isothermal Process

An isothermal process is one in which the temperature remains constant throughout. In such scenarios, according to the ideal gas law, any change in pressure necessitates a compensatory change in volume. This process is particularly important because it results in predictable relationships between work and volume changes when the system exchanges heat with an environment to maintain constant temperature.

Work in Thermodynamic Processes

In thermodynamics, the work done by or on a system due to volume changes is given by the integral of pressure with respect to volume (W = ?p dV). For an isothermal process involving an ideal gas, this expression can be evaluated using the ideal gas law, leading to a logarithmic relationship that quantifies how work depends on the ratio of final to initial volumes or pressures.