If the $r.m.s.$ velocity of a gas at a given temperature (Kelvin scale) is $300\, m/sec$. What will be the $r.m.s.$ velocity of a gas having twice the molecular weight and half the temperature on Kelvin scale ....... $m/sec$
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$Assertion :$ The root mean square and most probable speeds of the molecules in a gas are the same.
$Reason :$ The Maxwell distribution for the speed of molecules in a gas in symmetrical.
For an ideal gas the instantaneous change in pressure $'{p} '$ with volume $'v'$ is given by the equation $\frac{{dp}}{{dv}}=-{ap} .$ If ${p}={p}_{0}$ at ${v}=0$ is the given boundary condition, then the maximum temperature one mole of gas can attain is :
Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from $\tau_{1}$ to $\tau_{2} .$ If $\frac{C_{p}}{C_{v}}=\gamma$ for this gas then a good estimate for $\frac{\tau_{2}}{\tau_{1}}$ is given by :
One kg of a diatomic gas is at a pressure of $8 × 10^4\ N/m^2$. The density of the gas is $4\ kg/m^3$. What is the energy of the gas due to its thermal motion ?
$1$ mole of rigid diatomic gas performs a work of $Q / 5$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{ x R }{8},$ The value of $x$ is $\ldots \ldots \ldots .$ $[ K =$ universal gas constant $]$
Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium $M_1=4\ g$ and that of hydrogen $M_2=2\ g$ The equivalent degree of freedom $f$ of the mixture is