139163
The average kinetic energy of a monatomic gas molecule kept at temperature $27^{\circ} \mathrm{C}$ is (Boltzmann constant $\mathrm{k}=\mathbf{1 . 3} \times 10^{-23} \mathrm{JK}^{-1}$ )
1 $5.85 \times 10^{-21} \mathrm{~J}$
2 $4.12 \times 10^{-21} \mathrm{~J}$
3 $3.75 \times 10^{-21} \mathrm{~J}$
4 $2.85 \times 10^{-21} \mathrm{~J}$
5 $7.55 \times 10^{-21} \mathrm{~J}$
Explanation:
A Given that, $\mathrm{T}=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}$ We know that, Average kinetic energy of monatomic gas - $\mathrm{v}_{\mathrm{av}} =\frac{3}{2} \mathrm{kT}$ $=\frac{3}{2} \times 1.3 \times 10^{-23} \times 300$ $=\frac{9}{2} \times 1.3 \times 10^{-21}$ $\mathrm{v}_{\mathrm{av}}=5.85 \times 10^{-21} \mathrm{~J}$
Kerala CEE 2020
Kinetic Theory of Gases
139165
If the rms velocity of a perfect gas at $27^{\circ} \mathrm{C}$ is $500 \mathrm{~m} \cdot \mathrm{s}^{-1}$, the same at $927^{\circ} \mathrm{C}$ will be
139166
Equal volumes of hydrogen and oxygen gasses of atomic weights 1 and 16 respectively are found to exert equal pressure on the walls of two separate containers. The rms velocities of the two gasses are in the ratio
1 $1: 4$
2 $4: 1$
3 $1: 32$
4 $32: 1$
Explanation:
B Given, atomic weight of hydrogen $=1$ then molar mass of hydrogen $(\mathrm{M})=2 \mathrm {AMU}$ Ans: b : Given, Initial pressure $=\left(\mathrm{P}_{1}\right)=\mathrm{P}_{\mathrm{o}}$ Initial mass $\left(\mathrm{m}_{1}\right)=\mathrm{m}$ Initial rms velocity $\left(\mathrm{v}_{1}\right)_{\mathrm{rms}}=\mathrm{v}$ Final mass $\left(\mathrm{m}_{2}\right)=\mathrm{m} / 2$ Final rms velocity $\left(\mathrm{v}_{2}\right)_{\mathrm{rms}}=2 \mathrm{v}$ $\therefore \quad \mathrm{P} =\frac{1}{3} \frac{\mathrm{mNv}_{\mathrm{rms}}^{2}}{\mathrm{~V}}$ $\therefore \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\frac{1}{3} \mathrm{~m}_{1} \mathrm{~N}\left(\mathrm{v}_{1}\right)^{2}{ }_{\mathrm{rms}} \times \mathrm{V}}{\mathrm{V} \times \frac{1}{3} \mathrm{~m}_{2} \mathrm{~N}\left(\mathrm{v}_{2}\right)^{2}}$ $\frac{\mathrm{P}_{0}}{\mathrm{P}_{2}} =\frac{\mathrm{m} \mathrm{v}^{2}}{\mathrm{~m} / 2 \times(2 \mathrm{v})^{2}}=\frac{2}{4}$ $\frac{\mathrm{P}_{0}}{\mathrm{P}_{2}} =\frac{1}{2}$ $\mathrm{P}_{2} =2 \mathrm{P}_{\mathrm{o}}$
We know that
Kinetic Theory of Gases
139167
If $\bar{\lambda}$ is the mean free path, $m$ is the mass of the gas molecule, $\rho$ is the density of the gas, $T$ is the absolute temperature of the gas and $P$ is the pressure of the gas, then which of the following relation is false.
139163
The average kinetic energy of a monatomic gas molecule kept at temperature $27^{\circ} \mathrm{C}$ is (Boltzmann constant $\mathrm{k}=\mathbf{1 . 3} \times 10^{-23} \mathrm{JK}^{-1}$ )
1 $5.85 \times 10^{-21} \mathrm{~J}$
2 $4.12 \times 10^{-21} \mathrm{~J}$
3 $3.75 \times 10^{-21} \mathrm{~J}$
4 $2.85 \times 10^{-21} \mathrm{~J}$
5 $7.55 \times 10^{-21} \mathrm{~J}$
Explanation:
A Given that, $\mathrm{T}=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}$ We know that, Average kinetic energy of monatomic gas - $\mathrm{v}_{\mathrm{av}} =\frac{3}{2} \mathrm{kT}$ $=\frac{3}{2} \times 1.3 \times 10^{-23} \times 300$ $=\frac{9}{2} \times 1.3 \times 10^{-21}$ $\mathrm{v}_{\mathrm{av}}=5.85 \times 10^{-21} \mathrm{~J}$
Kerala CEE 2020
Kinetic Theory of Gases
139165
If the rms velocity of a perfect gas at $27^{\circ} \mathrm{C}$ is $500 \mathrm{~m} \cdot \mathrm{s}^{-1}$, the same at $927^{\circ} \mathrm{C}$ will be
139166
Equal volumes of hydrogen and oxygen gasses of atomic weights 1 and 16 respectively are found to exert equal pressure on the walls of two separate containers. The rms velocities of the two gasses are in the ratio
1 $1: 4$
2 $4: 1$
3 $1: 32$
4 $32: 1$
Explanation:
B Given, atomic weight of hydrogen $=1$ then molar mass of hydrogen $(\mathrm{M})=2 \mathrm {AMU}$ Ans: b : Given, Initial pressure $=\left(\mathrm{P}_{1}\right)=\mathrm{P}_{\mathrm{o}}$ Initial mass $\left(\mathrm{m}_{1}\right)=\mathrm{m}$ Initial rms velocity $\left(\mathrm{v}_{1}\right)_{\mathrm{rms}}=\mathrm{v}$ Final mass $\left(\mathrm{m}_{2}\right)=\mathrm{m} / 2$ Final rms velocity $\left(\mathrm{v}_{2}\right)_{\mathrm{rms}}=2 \mathrm{v}$ $\therefore \quad \mathrm{P} =\frac{1}{3} \frac{\mathrm{mNv}_{\mathrm{rms}}^{2}}{\mathrm{~V}}$ $\therefore \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\frac{1}{3} \mathrm{~m}_{1} \mathrm{~N}\left(\mathrm{v}_{1}\right)^{2}{ }_{\mathrm{rms}} \times \mathrm{V}}{\mathrm{V} \times \frac{1}{3} \mathrm{~m}_{2} \mathrm{~N}\left(\mathrm{v}_{2}\right)^{2}}$ $\frac{\mathrm{P}_{0}}{\mathrm{P}_{2}} =\frac{\mathrm{m} \mathrm{v}^{2}}{\mathrm{~m} / 2 \times(2 \mathrm{v})^{2}}=\frac{2}{4}$ $\frac{\mathrm{P}_{0}}{\mathrm{P}_{2}} =\frac{1}{2}$ $\mathrm{P}_{2} =2 \mathrm{P}_{\mathrm{o}}$
We know that
Kinetic Theory of Gases
139167
If $\bar{\lambda}$ is the mean free path, $m$ is the mass of the gas molecule, $\rho$ is the density of the gas, $T$ is the absolute temperature of the gas and $P$ is the pressure of the gas, then which of the following relation is false.
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Kinetic Theory of Gases
139163
The average kinetic energy of a monatomic gas molecule kept at temperature $27^{\circ} \mathrm{C}$ is (Boltzmann constant $\mathrm{k}=\mathbf{1 . 3} \times 10^{-23} \mathrm{JK}^{-1}$ )
1 $5.85 \times 10^{-21} \mathrm{~J}$
2 $4.12 \times 10^{-21} \mathrm{~J}$
3 $3.75 \times 10^{-21} \mathrm{~J}$
4 $2.85 \times 10^{-21} \mathrm{~J}$
5 $7.55 \times 10^{-21} \mathrm{~J}$
Explanation:
A Given that, $\mathrm{T}=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}$ We know that, Average kinetic energy of monatomic gas - $\mathrm{v}_{\mathrm{av}} =\frac{3}{2} \mathrm{kT}$ $=\frac{3}{2} \times 1.3 \times 10^{-23} \times 300$ $=\frac{9}{2} \times 1.3 \times 10^{-21}$ $\mathrm{v}_{\mathrm{av}}=5.85 \times 10^{-21} \mathrm{~J}$
Kerala CEE 2020
Kinetic Theory of Gases
139165
If the rms velocity of a perfect gas at $27^{\circ} \mathrm{C}$ is $500 \mathrm{~m} \cdot \mathrm{s}^{-1}$, the same at $927^{\circ} \mathrm{C}$ will be
139166
Equal volumes of hydrogen and oxygen gasses of atomic weights 1 and 16 respectively are found to exert equal pressure on the walls of two separate containers. The rms velocities of the two gasses are in the ratio
1 $1: 4$
2 $4: 1$
3 $1: 32$
4 $32: 1$
Explanation:
B Given, atomic weight of hydrogen $=1$ then molar mass of hydrogen $(\mathrm{M})=2 \mathrm {AMU}$ Ans: b : Given, Initial pressure $=\left(\mathrm{P}_{1}\right)=\mathrm{P}_{\mathrm{o}}$ Initial mass $\left(\mathrm{m}_{1}\right)=\mathrm{m}$ Initial rms velocity $\left(\mathrm{v}_{1}\right)_{\mathrm{rms}}=\mathrm{v}$ Final mass $\left(\mathrm{m}_{2}\right)=\mathrm{m} / 2$ Final rms velocity $\left(\mathrm{v}_{2}\right)_{\mathrm{rms}}=2 \mathrm{v}$ $\therefore \quad \mathrm{P} =\frac{1}{3} \frac{\mathrm{mNv}_{\mathrm{rms}}^{2}}{\mathrm{~V}}$ $\therefore \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\frac{1}{3} \mathrm{~m}_{1} \mathrm{~N}\left(\mathrm{v}_{1}\right)^{2}{ }_{\mathrm{rms}} \times \mathrm{V}}{\mathrm{V} \times \frac{1}{3} \mathrm{~m}_{2} \mathrm{~N}\left(\mathrm{v}_{2}\right)^{2}}$ $\frac{\mathrm{P}_{0}}{\mathrm{P}_{2}} =\frac{\mathrm{m} \mathrm{v}^{2}}{\mathrm{~m} / 2 \times(2 \mathrm{v})^{2}}=\frac{2}{4}$ $\frac{\mathrm{P}_{0}}{\mathrm{P}_{2}} =\frac{1}{2}$ $\mathrm{P}_{2} =2 \mathrm{P}_{\mathrm{o}}$
We know that
Kinetic Theory of Gases
139167
If $\bar{\lambda}$ is the mean free path, $m$ is the mass of the gas molecule, $\rho$ is the density of the gas, $T$ is the absolute temperature of the gas and $P$ is the pressure of the gas, then which of the following relation is false.
139163
The average kinetic energy of a monatomic gas molecule kept at temperature $27^{\circ} \mathrm{C}$ is (Boltzmann constant $\mathrm{k}=\mathbf{1 . 3} \times 10^{-23} \mathrm{JK}^{-1}$ )
1 $5.85 \times 10^{-21} \mathrm{~J}$
2 $4.12 \times 10^{-21} \mathrm{~J}$
3 $3.75 \times 10^{-21} \mathrm{~J}$
4 $2.85 \times 10^{-21} \mathrm{~J}$
5 $7.55 \times 10^{-21} \mathrm{~J}$
Explanation:
A Given that, $\mathrm{T}=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}$ We know that, Average kinetic energy of monatomic gas - $\mathrm{v}_{\mathrm{av}} =\frac{3}{2} \mathrm{kT}$ $=\frac{3}{2} \times 1.3 \times 10^{-23} \times 300$ $=\frac{9}{2} \times 1.3 \times 10^{-21}$ $\mathrm{v}_{\mathrm{av}}=5.85 \times 10^{-21} \mathrm{~J}$
Kerala CEE 2020
Kinetic Theory of Gases
139165
If the rms velocity of a perfect gas at $27^{\circ} \mathrm{C}$ is $500 \mathrm{~m} \cdot \mathrm{s}^{-1}$, the same at $927^{\circ} \mathrm{C}$ will be
139166
Equal volumes of hydrogen and oxygen gasses of atomic weights 1 and 16 respectively are found to exert equal pressure on the walls of two separate containers. The rms velocities of the two gasses are in the ratio
1 $1: 4$
2 $4: 1$
3 $1: 32$
4 $32: 1$
Explanation:
B Given, atomic weight of hydrogen $=1$ then molar mass of hydrogen $(\mathrm{M})=2 \mathrm {AMU}$ Ans: b : Given, Initial pressure $=\left(\mathrm{P}_{1}\right)=\mathrm{P}_{\mathrm{o}}$ Initial mass $\left(\mathrm{m}_{1}\right)=\mathrm{m}$ Initial rms velocity $\left(\mathrm{v}_{1}\right)_{\mathrm{rms}}=\mathrm{v}$ Final mass $\left(\mathrm{m}_{2}\right)=\mathrm{m} / 2$ Final rms velocity $\left(\mathrm{v}_{2}\right)_{\mathrm{rms}}=2 \mathrm{v}$ $\therefore \quad \mathrm{P} =\frac{1}{3} \frac{\mathrm{mNv}_{\mathrm{rms}}^{2}}{\mathrm{~V}}$ $\therefore \quad \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}} =\frac{\frac{1}{3} \mathrm{~m}_{1} \mathrm{~N}\left(\mathrm{v}_{1}\right)^{2}{ }_{\mathrm{rms}} \times \mathrm{V}}{\mathrm{V} \times \frac{1}{3} \mathrm{~m}_{2} \mathrm{~N}\left(\mathrm{v}_{2}\right)^{2}}$ $\frac{\mathrm{P}_{0}}{\mathrm{P}_{2}} =\frac{\mathrm{m} \mathrm{v}^{2}}{\mathrm{~m} / 2 \times(2 \mathrm{v})^{2}}=\frac{2}{4}$ $\frac{\mathrm{P}_{0}}{\mathrm{P}_{2}} =\frac{1}{2}$ $\mathrm{P}_{2} =2 \mathrm{P}_{\mathrm{o}}$
We know that
Kinetic Theory of Gases
139167
If $\bar{\lambda}$ is the mean free path, $m$ is the mass of the gas molecule, $\rho$ is the density of the gas, $T$ is the absolute temperature of the gas and $P$ is the pressure of the gas, then which of the following relation is false.