If the absolute temperature of a gas is increased $5$ times,the r.m.s. velocity of the gas molecules will be

The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200 \, m/s$ at $27^{\circ}C$ and $1.0 \times 10^5 \, N/m^2$ pressure. When the temperature is $127^{\circ}C$ and pressure is $0.5 \times 10^5 \, N/m^2$,the $r.m.s.$ velocity in $m/s$ will be

The average speed $\bar{v}$ and $r.m.s.$ speed $v_{rms}$ of the molecules are related as

Define absolute temperature.

The speeds of ten particles in $ms^{-1}$ are $0, 2, 3, 4, 4, 4, 5, 5, 6, 9$. The values of average speed,$rms$ speed,and most probable speed are respectively:

The temperature at which the root mean square velocity of hydrogen molecules equals their escape velocity from the Earth is closest to: [Boltzmann constant $k_B = 1.38 \times 10^{-23} \, J/K$,Avogadro number $N_A = 6.02 \times 10^{23} \, mol^{-1}$,Molar mass of $H_2 = 2 \times 10^{-3} \, kg/mol$,Radius of Earth $R_e = 6.4 \times 10^6 \, m$,Gravitational acceleration $g = 10 \, m/s^2$]