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The temperature of a gas is $-78^{\circ} \mathrm{C}$ and the average translational kinetic energy of its molecules is $\mathrm{K}$. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $2 \mathrm{~K}$ is :
Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed $\left(v_{ ms }\right)$ and choose the correct answer from the options given below:
Two containers $C_{1}$ and $C_{2}$ of volumes $V$ and $4 \,V$ respectively, hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in $C_{1}$ and $C_{2}$ are $p$ and $5 p$, respectively. Heat baths are employed to maintain the temperatures in the containers at $300 \,K$ and $400 \,K$, respectively. The valve is now opened. Select the correct statement.
When an air bubble of radius $‘r’$ rises from the bottom to the surface of a lake, its radius becomes $5r/4$ (the pressure of the atmosphere is equal to the $10 \,m$ height of water column). If the temperature is constant and the surface tension is neglected, the depth of the lake is .... $m$
One mole of an ideal gas $\left( {\frac{{{C_P}}}{{{C_V}}}\, = \gamma } \right)$ heated by law $P=\alpha V$ where $P$ is pressure of gas, $V$ is volume, $\alpha$ is a constant what is the heat capacity of gas in the process-
A cylindrical tube of cross-sectional area $A$ has two air tight frictionless pistons at its two ends. The pistons are tied with a straight two ends. The pistons are tied with a straight piece of metallic wire. The tube contains a gas at atmospheric pressure $P_0$ and temperature $T_0$. If temperature of the gas is doubled then the tension in the wire is
The plot that depicts the behavior of the mean free time $t$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature $(T)$, qualitatively, is (Graphs are schematic and not drawn to scale)
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 $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ):