The density of water is $1000 \; kg \; m^{-3}$. The density of water vapour at $100 \; ^{\circ}C$ and $1 \; atm$ pressure is $0.6 \; kg \; m^{-3}$. The volume of a molecule multiplied by the total number gives what is called molecular volume. Estimate the ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure.
- A$6 \times 10^{-4}$
- B$6 \times 10^{-3}$
- C$6 \times 10^{-5}$
- D$6 \times 10^{-2}$
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One mole of the ideal gas goes through the process $p=p_0\left[1-\alpha\left(\frac{V}{V_0}\right)^3\right]$, where $p$ and $V$ are pressure and volume, $p_0, V_0$ and $\alpha$ are constants. If the maximum attainable temperature of the gas is $\left(\frac{3}{4}\right) \frac{p_0 V_0}{R}$, then the value of $\alpha$ is
DifficultTS EAMCET 2018
View SolutionIn the kinetic theory of gases,which of these statements is/are true?
$(i)$ The pressure of a gas is proportional to the mean speed of the molecules.
$(ii)$ The root mean square speed of the molecules is proportional to the pressure.
$(iii)$ The rate of diffusion is proportional to the mean speed of the molecules.
$(iv)$ The mean translational kinetic energy of a gas is proportional to its kelvin temperature.
$(i)$ The pressure of a gas is proportional to the mean speed of the molecules.
$(ii)$ The root mean square speed of the molecules is proportional to the pressure.
$(iii)$ The rate of diffusion is proportional to the mean speed of the molecules.
$(iv)$ The mean translational kinetic energy of a gas is proportional to its kelvin temperature.
Medium
View Solution$A$ flask contains argon and chlorine in the ratio of $2: 1$ by mass. The temperature of the mixture is $27\,^{\circ}C$. Obtain the ratio of
$(i)$ average kinetic energy per molecule,and
$(ii)$ root mean square speed $v_{rms}$ of the molecules of the two gases.
Atomic mass of argon $= 39.9\,u$; Molecular mass of chlorine $= 70.9\,u$.
$(i)$ average kinetic energy per molecule,and
$(ii)$ root mean square speed $v_{rms}$ of the molecules of the two gases.
Atomic mass of argon $= 39.9\,u$; Molecular mass of chlorine $= 70.9\,u$.
Medium
View Solution$0.056 \, kg$ of Nitrogen is enclosed in a vessel at a temperature of $127 \, ^{\circ}C$. The amount of heat required to double the speed of its molecules is $k \, cal$. (Take $R = 2 \, cal \, mole^{-1} K^{-1}$)
The mass of a hydrogen atom is $3.32 \times 10^{-27} \, kg$. If $10^{23}$ atoms per second strike a wall of area $2 \, cm^2$ at an angle of $45^{\circ}$ with the normal to the wall and reflect elastically with a speed of $10^3 \, m/s$,the pressure exerted on the wall will be: $(N/m^2)$
Medium
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