The equation of state of an ideal gas is P V=n R T, where n...

The equation of state of an ideal gas is $P V=n R T$, where $n$ and $R$ are constants.
(a) Show that the volume expansivity $\beta$ is equal to $1 / T$.
(b) Show that the isothermal compressibility $\kappa$ is equal to $1 / P$.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Volume Expansivity

Volume expansivity, often denoted by ?, is a thermodynamic property that measures the fractional change in volume per unit change in temperature at constant pressure. Mathematically, it is expressed as ? = (1/V)(?V/?T)_P. It quantifies how the volume of a substance expands as its temperature increases, which is particularly straightforward to compute for systems described by the ideal gas law.

Isothermal Compressibility

Isothermal compressibility, denoted by ?, is defined as the relative change in volume per unit change in pressure at constant temperature. It is given by the equation ? = -(1/V)(?V/?P)_T. This property describes how much a fluid or gas compresses when the pressure is increased, and its calculation for an ideal gas leads to a simple relationship due to the linear dependency between pressure and volume in the ideal gas equation.

Ideal Gas Law

The Ideal Gas Law, given by PV = nRT, is a fundamental equation in thermodynamics that relates the pressure, volume, and temperature of an ideal gas. It serves as an equation of state by providing a model for predicting the behavior of a gas when its state variables change, under the assumption that the gas particles do not interact except through elastic collisions.

Transcript

Please give Ace some feedback