Consider a hypothetical gas with molecules that can move along only a single axis. The following table gives four situations, the velocities in meter per second of such a gas having four molecules. The plus and minus sign refer to the direction of the velocity along the axis.

In which situation the root-mean-square speed of the molecules is greatest?

One mole of an ideal gas is kept enclosed under a light piston$(\text{area}={10}^{–2} {\mathrm{m}}^2 )$ connected by a compressed spring (spring constant $100 \mathrm{N} {\mathrm{m}}^{-1}$). The volume of gas is $0.83 {\mathrm{m}}^3$ and its temperature is $100 \mathrm{K}$. The gas is heated so that it compresses the spring further by $0.1 \mathrm{m}.$The work done by the gas in the process is $\mathrm{N}\times {10}^{–1} \mathrm{J}.$ Find $\mathrm{N}$. (Take $R=8.3 \mathrm{J} {\mathrm{K}}^{-1}-\mathrm{mole}$ and suppose there is no atmosphere).