One mole of ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5).$ What is $\gamma $ for the mixture$?$ $\gamma $ denotes the ratio of specific heat at constant pressure, to that at constant volume
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A flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ} C$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :
A diatomic gas of molecular mass $40 \,g / mol$ is filled in a rigid container at temperature $30^{\circ} C$. It is moving with velocity $200 \,m / s$. If it is suddenly stopped, the rise in the temperature of the gas is .........
A given mass of a gas is allowed to expand freely until its volume becomes double. If ${C_b}$ and ${C_a}$ are the velocities of sound in this gas before and after expansion respectively, then ${C_a}$ is equal to
An insulated box containing a diatomic gas of molar mass $M$ is moving with a velocity $v$. The box is suddenly stopped. The resulting change in temperature is
A jar contains a gas and few drops of water at $T K.$ The pressure in the jar is $830 \,mm$ of mercury. The temperature of jar is reduced by $1\%.$ The saturated vapour pressure of water at the two temperatures are $30 \,mm$ and $ 25\, mm$ of mercury. Then the new pressure in the jar will be ..... $mm$ of $Hg$
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. . . . . .
A gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of $RT$ ) of the mixture is