The temperature of an ideal gas is increased from $120\, K$ to $480\, K.$ If at $120\, K,$ the root mean square velocity of the gas molecules is $v,$ at $480\, K$ it becomes
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A spherical bubble inside water has radius $R$. Take the pressure inside the bubble and the water pressure to be $p_0$. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes $(R-a)$. For $a \ll R$ the magnitude of the work done in the process is given by $\left(4 \pi p_0 R a^2\right) X$, where $X$ is a constant and $\gamma=C_p / C_V=41 / 30$. The value of $X$ is. . . . . .
Modern vacuum pumps can evacuate a vessel down to a pressure of $4.0 \times {10^{ - 15}}\, atm$ at room temperature $(300\, K)$. Taking $R = 8.0\, JK^{-1}\, mole^{-1}$ , $1\, atm = 10^5\, Pa$ and $N_ {Avogadro} = 6 \times 10^{23}\, mole^{-1}$ , the mean distance between molecules of gas in an evacuated vessel will be of the order of
The lowest pressure (the best Vacuum) that can be created in the laboratory at $27$ degree is $10^{-11} \;{mm}$ of $Hg$. At this pressure, the number of ideal gas molecules per ${cm}^{3}$ will be
The number density of molecules of a gas depends on their distance $r$ from the origin as, $n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}$. Then the total number of molecules is proportional to
The pressure and temperature of an ideal gas in a closed vessel are $720\, kPa$ and $40^oC$ respectively. If $\frac{1}{4}^{th}$ of the gas is released from the vessel and the temperature of the remaining gas is raised to $353^oC,$ the final pressure of the gas is ....... $kPa$
$Assertion :$ Mean free path of a gas molecules varies inversely as density of the gas.
$Reason :$ Mean free path varies inversely as pressure of the gas.
A container $X$ has volume double that of contianer $Y$ and both are connected by a thin tube. Both contains same ideal gas. The temperature of $X$ is $200\,\,K$ and that of $Y$ is $400\,\,K$. If mass of gas in $X$ is $m$ then in $Y$ it will be:
Let $\bar v , \bar v_{rms}$ and $v_p$ respectively denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T$. The mass of the molecule is $m$. Then