A container holds 1 million helium molecules at $300 \mathrm{~K}$. If we double the gas's temperature to $600 \mathrm{~K}$, by about what factor does its multiplicity increase?

Question

Quizplus · Accepted Answer

The multiplicity of an ideal gas is proportional to $T^{3N/2}$, where $N$ is the number of molecules. Doubling the temperature from 300 K to 600 K increases the multiplicity by a factor of $2^{3N/2}$. With $N = 1,000,000$, the factor is $2^{1,500,000}$.

A Container Holds 1 Million Helium Molecules At 300 K300 \mathrm{~K}300 K If We Double the Gas's Temperature To 300

A Container Holds 1 Million Helium Molecules At $300 \mathrm{~K}$ If We Double the Gas's Temperature To 300