Suppose that we allow an ideal gas containing $N$ atoms to expand slowly and isothermally to twice its initial volume. By what factor does its multiplicity increase?
A) By a factor of 2 .
B) By a factor of $2^{N}$.
C) The multiplicity does not change.
D) The answer depends on the gas's initial volume.
E) The answer depends on the gas's fixed temperature.

Question

Quizplus · Accepted Answer

The multiplicity of an ideal gas, which is a measure of the number of microstates corresponding to a given macrostate, increases exponentially with volume for a given number of particles and temperature. When an ideal gas expands isothermally to twice its initial volume, its multiplicity increases by a factor of $2^N$, where $N$ is the number of particles in the gas. This is because each particle has twice as many positions it can occupy, leading to an exponential increase in the total number of microstates.

Suppose That We Allow an Ideal Gas Containing NNN Atoms to Expand Slowly and Isothermally to Twice Its Initial

Suppose That We Allow an Ideal Gas Containing $N$ Atoms to Expand Slowly and Isothermally to Twice Its Initial