(B) Let $N_0 = 1000 \text{ molecules}/m^3$ be the initial concentration.In one minute,the number of molecules leaving is $\frac{1}{10} N_0$. Thus,the

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(B) Let $N_0 = 1000 \text{ molecules}/m^3$ be the initial concentration.In one minute,the number of molecules leaving is $\frac{1}{10} N_0$. Thus,the remaining concentration after $1 \text{ minute}$ is $N_1 = N_0 - \frac{1}{10} N_0 = \frac{9}{10} N_0 = 0.9 N_0$.This follows the discrete decay model $N_t = N_0(0.9)^t$,where $t$ is in minutes.We want to find $t$ such that $N_t = 1 \text{ molecule}/m^3$.$1 = 1000(0.9)^t$$(0.9)^t = 0.001$Taking the natural logarithm on both sides:$t \ln(0.9) = \ln(0.001)$$t \approx \frac{-6.9077}{-0.10536} \approx 65.56 \text{ minutes}$.Rounding to the nearest provided option,$t \approx 70 \text{ minutes}$.

Class 11 Physics Kinetic Theory of Gases Mix Examples-Kinetic Theory of Gases

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In saloons,there is always a characteristic smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \text{ molecules}/m^3$. Due to air ventilation,the number of molecules leaving in one minute is one-tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \text{ molecule}/m^3$?

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A
$7$ minutes
B
$70$ minutes
C
$100$ minutes
D
Very long time which cannot be calculated.

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Kinetic Theory of Gases

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Mix Examples-Kinetic Theory of Gases

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$2.8 \ g$ of nitrogen gas $(N_2)$ is in a vessel at a temperature of $127^{\circ} C$. The amount of heat energy required to increase the rms speed of the nitrogen molecules by $41.4 \%$ is $(R = 8.31 \ J \ mol^{-1} \ K^{-1})$. (in $J$)

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If the pressure of $CO_2$ (real gas) in a container is given by $P = \frac{RT}{2V - b} - \frac{a}{4V^2}$,then the mass of the gas in the container is ...... $g$.

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Two thermally insulated vessels $1$ and $2$ contain air at temperatures $(T_1, T_2)$,volumes $(V_1, V_2)$,and pressures $(P_1, P_2)$. If the valve connecting them is opened,what will be the equilibrium temperature of the system?

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$A$ molecule in a gas container hits a horizontal wall with speed $200 \; m s^{-1}$ at an angle of $30^{\circ}$ with the normal,and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?

Medium

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Following statements are given:
$(1)$ The average kinetic energy of a gas molecule decreases when the temperature is reduced.
$(2)$ The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
$(3)$ The average kinetic energy of a gas molecule decreases with increase in volume.
$(4)$ Pressure of a gas increases with increase in temperature at constant volume.
$(5)$ The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:

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$2.8 \ g$ of nitrogen gas $(N_2)$ is in a vessel at a temperature of $127^{\circ} C$. The amount of heat energy required to increase the rms speed of the nitrogen molecules by $41.4 \%$ is $(R = 8.31 \ J \ mol^{-1} \ K^{-1})$. (in $J$)

If the pressure of $CO_2$ (real gas) in a container is given by $P = \frac{RT}{2V - b} - \frac{a}{4V^2}$,then the mass of the gas in the container is ...... $g$.

Two thermally insulated vessels $1$ and $2$ contain air at temperatures $(T_1, T_2)$,volumes $(V_1, V_2)$,and pressures $(P_1, P_2)$. If the valve connecting them is opened,what will be the equilibrium temperature of the system?

$A$ molecule in a gas container hits a horizontal wall with speed $200 \; m s^{-1}$ at an angle of $30^{\circ}$ with the normal,and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?

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