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A spherical soap bubble inside an air chamber at pressure $P_0=10^5 Pa$ has a certain radius so that the excess pressure inside the bubble is $\Delta P=144 Pa$. Now, the chamber pressure is reduced to $8 P_0 / 27$ so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure $\Delta P$ in both the cases to be much smaller than the chamber pressure. The new excess pressure $\Delta P$ in $Pa$ is
A cylinder of capacity $20$ litres is filled with ${H_2}$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5 \times {10^5}\,J$. The pressure of hydrogen in the cylinder is
$STATEMENT- 1$ The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and its volume. because
$STATEMENT-2$ The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.
A gas consisting of a rigid diatomic molecules was initially under standard condition. Then, gas was compressed adiabatically to one$-$fifth of its initial volume. What will be the mean kinetic energy of a rotating molecule in the final state ?
$1$ 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 $]$