EVALUATION

If the rms speed of methane gas in the Jupiter's atmosphere is $471.8 \mathrm{m}/\mathrm{s}$, show that the surface temperature of Jupiter is sub-zero.

Calculate the temperature at which the rms velocity of a gas triples its value at S.T.P.

A gas is at temperature $80°C$ and pressure $5 \times {10}^{-10} N/m^2.$ What is the number of molecules per $m^3.$

If ${10}^{20}$ oxygen molecules per second strike $4 {\mathrm{cm}}^2$ of wall at an angle of $30°$ with the normal when moving at a speed of $2 \times {10}^3 \mathrm{m}/\mathrm{s}$, find the pressure exerted on the wall. Mass of one oxygen atom = $2.67 \times {10}^{-26 }kg$

During an adiabatic process, the pressure of a mixture of monatomic and diatomic gases is found to be proportional to the cube of the temperature. Find the value of $\gamma =\raisebox{1ex}{$C_p$}\!\left/ \!\raisebox{-1ex}{$C_v$}\right.$.

Calculate the mean free path of air molecules at STP. The diameter of ${\mathrm{N}}_2 \mathrm{and} {\mathrm{O}}_2$ is about $3\times {10}^{-10} \mathrm{m}$.

A gas made of a mixture of $2 \mathrm{moles}$ of oxygen and $4 \mathrm{moles}$ of argon at temperature $T$. Calculate the energy of the gas in terms of $R \mathrm{and} T$ where $R$ is Boltzmann's constant. Neglect the vibrational modes.

Estimate the total number of air molecules in a room of capacity $25 m^3$ at a temperature of $27°C$.