An $HCl$ molecule has rotational, translational and vibrational motions. If the $rms$ velocity of $HCl$ molecules in its gaseous phase is $\bar v ,\,m$ is its mass and $k_B$ is Boltzmann constant, then its temperature will be
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A box containing $N$ molecules of a perfect gas at temperature ${T_1}$ and pressure ${P_1}$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is ${P_2}$ and temperature ${T_2}$, then
When the temperature of a gas is raised from $27^o C$ to $90^o C$, the percentage increase in the $r.m.s.$ velocity of the molecules will be ..... $\%$
A gas at $27^o C$ has a volume $V$ and pressure $P.$ On heating its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be ...... $^oC$
$105$ calories of heat is required to raise the temperature of $3$ moles of an ideal gas at constant pressure from $30^{\circ} C$ to $35^{\circ} C$. The amount of heat required in calories to raise the temperature of the gas through the range $\left(60^{\circ} C\right.$ to $\left.65^{\circ} C \right)$ at constant volume is ........ $cal$ $\left(\gamma=\frac{C_p}{C_v}=1.4\right)$
A cylinder of fixed capacity of $44.8 \,litres$ contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by $20.0^{\circ} C$ will be .............. $J$(Given gas constant $R =8.3 \,JK ^{-1}- moI ^{-1}$ )