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At a pressure of $24 \times {10^5}\,dyne/c{m^2}$, the volume of ${O_2}$ is $10\, litre$ and mass is $20\, gm.$ The $r.m.s.$ velocity will be....... $m/sec$
The following graph represents the $T-V$ curves of an ideal gas (where $T$ is the temperature and $V$ the volume) at three pressures $P_1, P_2$ and $P_3$ compared with those of Charles's law represented as dotted lines.
An object is placed in a medium of refractive index $3$. An electromagnetic wave of intensity $6 \times 10^8 \mathrm{~W} / \mathrm{m}^2$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ):
The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0°C$ is $3180$ metres/second. The pressure on the hydrogen gas is ..... $atm$ (Density of hydrogen gas is $8.99 \times {10^{ - 2}}\,kg/{m^3}$, $1$ atmosphere $ = 1.01 \times {10^5}\,N/{m^2})$
The temperature of the hydrogen at which the average speed of its molecules is equal to that of oxygen molecules at a temperature of $31\,^oC,$ is ........ $^oC$
$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).
$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.
The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200\, m/sec$ at $27°C$ and $1.0 \times {10^5}\,N/{m^2}$ pressure. When the temperature is $127°C$ and pressure is $0.5 \times {10^5}\,N/{m^2}$, the $r.m.s.$ velocity in $m/sec$ will be
$\mathrm{N}$ moles of a polyatomic gas $(f=6)$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $\mathrm{N}$ is:
If $\mathrm{n}$ is the number density and $\mathrm{d}$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :