A sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T,$ the mass of each molecule is $m.$ The expression for the density of gas is ($k =$ Boltzmann’s constant)
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Let $\bar v,\;{v_{rms}}$ 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 a molecule is $m.$ Then
Two moles of an ideal gas with $\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3}$ are mixed with $3$ moles of another ideal gas with $\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{4}{3} .$ The value of $\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}$ for the mixture is
A volume $V$ and pressure $P$ diagram was obtained from state $1$ to state $2$ when a given mass of a gas is subjected to temperature changes. During this process the gas is
Let $A$ and $B$ the two gases and given : $\frac{{{T_A}}}{{{M_A}}} = 4.\frac{{{T_B}}}{{{M_B}}};$ where $T$ is the temperature and M is molecular mass. If ${C_A}$ and ${C_B}$ are the $r.m.s. $ speed, then the ratio $\frac{{{C_A}}}{{{C_B}}}$ will be equal to
$P-T$ diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct :
A balloon carries a total load of $185\; {kg}$ at normal pressure and temperature of $27^{\circ} {C}$. What load will the balloon carry on rising to a height at which the barometric pressure is $45\; {cm}$ of ${Hg}$ and the temperature is $-7^{\circ} {C}$. Assuming the volume constant? (in ${kg}$)