139249
The root-mean- square speed and average kinetic energy of the molecules of an ideal gas at absolute temperature $T$ are respectively proportional to
1 $\mathrm{T}$ and $\mathrm{T}^{-1}$
2 $\sqrt{\mathrm{T}}$ and $\mathrm{T}$
3 $\mathrm{T}$ and $\mathrm{T}^{2}$
4 $\mathrm{T}^{-1}$ and $\mathrm{T}$
Explanation:
B The root mean square speed of molecule is given as, $\mathrm{v}_{\text {rms }}=\sqrt{\frac{3 R T}{M}}$ $\mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$ Average kinetic energy (K.E.) $=\frac{3}{2} \mathrm{KT}$ $\therefore \quad$ K.E. $\propto \mathrm{T}$
SCRA-2013
Kinetic Theory of Gases
139255
The average energy per molecule of a triatomic gas at room temperature $T$ is
1 $3 \mathrm{kT}$
2 $\frac{1}{2} \mathrm{kT}$
3 $\frac{3}{2} \mathrm{kT}$
4 $\frac{5}{2} \mathrm{kT}$
Explanation:
A At room temperature $\mathrm{T}$ the degrees of freedom of triatomic gas $\mathrm{f}=6$ (3rotatonal, 3translation) So, $\text { Energy }=\frac{f}{2} K T$ $E=\frac{6}{2} K T=3 K T$
J and K-CET-2016
Kinetic Theory of Gases
139260
If the rms velocity of hydrogen gas at a certain temperature is $c$, then the rms velocity of oxygen gas at the same temperature is
1 $\frac{\mathrm{c}}{8}$
2 $\frac{\mathrm{c}}{10}$
3 $\frac{\mathrm{c}}{4}$
4 $\frac{\mathrm{c}}{2}$
Explanation:
C Molar mass of oxygen $=32$ Molar mass of Hydrogen $=2$ RMS velocity $\left(\mathrm{v}_{\mathrm{rms}}\right)=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{1}{\mathrm{M}}}$ Now, $\frac{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{O}_{2}}}{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{H}_{2}}}=\sqrt{\frac{\frac{1}{\frac{32}{1}}}{\frac{1}{2}}}=\frac{1}{4}$ $\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}=\frac{\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}{4}=\frac{\mathrm{C}}{4}$
WB JEE 2016
Kinetic Theory of Gases
139263
At what temperature will be rms speed of air molecules be double that of NTP?
139264
Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units respectively. The rms speed is
1 4 units
2 1.7 units
3 4.2 units
4 5 units
Explanation:
C Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{v}_{1}^{2}+\mathrm{v}_{2}^{2}+\ldots \ldots .+\mathrm{v}_{\mathrm{n}}^{2}}{\mathrm{n}}}$ $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{4+25+9+36+9+25}{6}}=\sqrt{\frac{108}{6}}=\sqrt{18}=3 \sqrt{2}$ $\mathrm{v}_{\mathrm{rms}}=3 \times 1.414=4.242$ units
139249
The root-mean- square speed and average kinetic energy of the molecules of an ideal gas at absolute temperature $T$ are respectively proportional to
1 $\mathrm{T}$ and $\mathrm{T}^{-1}$
2 $\sqrt{\mathrm{T}}$ and $\mathrm{T}$
3 $\mathrm{T}$ and $\mathrm{T}^{2}$
4 $\mathrm{T}^{-1}$ and $\mathrm{T}$
Explanation:
B The root mean square speed of molecule is given as, $\mathrm{v}_{\text {rms }}=\sqrt{\frac{3 R T}{M}}$ $\mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$ Average kinetic energy (K.E.) $=\frac{3}{2} \mathrm{KT}$ $\therefore \quad$ K.E. $\propto \mathrm{T}$
SCRA-2013
Kinetic Theory of Gases
139255
The average energy per molecule of a triatomic gas at room temperature $T$ is
1 $3 \mathrm{kT}$
2 $\frac{1}{2} \mathrm{kT}$
3 $\frac{3}{2} \mathrm{kT}$
4 $\frac{5}{2} \mathrm{kT}$
Explanation:
A At room temperature $\mathrm{T}$ the degrees of freedom of triatomic gas $\mathrm{f}=6$ (3rotatonal, 3translation) So, $\text { Energy }=\frac{f}{2} K T$ $E=\frac{6}{2} K T=3 K T$
J and K-CET-2016
Kinetic Theory of Gases
139260
If the rms velocity of hydrogen gas at a certain temperature is $c$, then the rms velocity of oxygen gas at the same temperature is
1 $\frac{\mathrm{c}}{8}$
2 $\frac{\mathrm{c}}{10}$
3 $\frac{\mathrm{c}}{4}$
4 $\frac{\mathrm{c}}{2}$
Explanation:
C Molar mass of oxygen $=32$ Molar mass of Hydrogen $=2$ RMS velocity $\left(\mathrm{v}_{\mathrm{rms}}\right)=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{1}{\mathrm{M}}}$ Now, $\frac{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{O}_{2}}}{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{H}_{2}}}=\sqrt{\frac{\frac{1}{\frac{32}{1}}}{\frac{1}{2}}}=\frac{1}{4}$ $\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}=\frac{\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}{4}=\frac{\mathrm{C}}{4}$
WB JEE 2016
Kinetic Theory of Gases
139263
At what temperature will be rms speed of air molecules be double that of NTP?
139264
Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units respectively. The rms speed is
1 4 units
2 1.7 units
3 4.2 units
4 5 units
Explanation:
C Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{v}_{1}^{2}+\mathrm{v}_{2}^{2}+\ldots \ldots .+\mathrm{v}_{\mathrm{n}}^{2}}{\mathrm{n}}}$ $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{4+25+9+36+9+25}{6}}=\sqrt{\frac{108}{6}}=\sqrt{18}=3 \sqrt{2}$ $\mathrm{v}_{\mathrm{rms}}=3 \times 1.414=4.242$ units
139249
The root-mean- square speed and average kinetic energy of the molecules of an ideal gas at absolute temperature $T$ are respectively proportional to
1 $\mathrm{T}$ and $\mathrm{T}^{-1}$
2 $\sqrt{\mathrm{T}}$ and $\mathrm{T}$
3 $\mathrm{T}$ and $\mathrm{T}^{2}$
4 $\mathrm{T}^{-1}$ and $\mathrm{T}$
Explanation:
B The root mean square speed of molecule is given as, $\mathrm{v}_{\text {rms }}=\sqrt{\frac{3 R T}{M}}$ $\mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$ Average kinetic energy (K.E.) $=\frac{3}{2} \mathrm{KT}$ $\therefore \quad$ K.E. $\propto \mathrm{T}$
SCRA-2013
Kinetic Theory of Gases
139255
The average energy per molecule of a triatomic gas at room temperature $T$ is
1 $3 \mathrm{kT}$
2 $\frac{1}{2} \mathrm{kT}$
3 $\frac{3}{2} \mathrm{kT}$
4 $\frac{5}{2} \mathrm{kT}$
Explanation:
A At room temperature $\mathrm{T}$ the degrees of freedom of triatomic gas $\mathrm{f}=6$ (3rotatonal, 3translation) So, $\text { Energy }=\frac{f}{2} K T$ $E=\frac{6}{2} K T=3 K T$
J and K-CET-2016
Kinetic Theory of Gases
139260
If the rms velocity of hydrogen gas at a certain temperature is $c$, then the rms velocity of oxygen gas at the same temperature is
1 $\frac{\mathrm{c}}{8}$
2 $\frac{\mathrm{c}}{10}$
3 $\frac{\mathrm{c}}{4}$
4 $\frac{\mathrm{c}}{2}$
Explanation:
C Molar mass of oxygen $=32$ Molar mass of Hydrogen $=2$ RMS velocity $\left(\mathrm{v}_{\mathrm{rms}}\right)=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{1}{\mathrm{M}}}$ Now, $\frac{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{O}_{2}}}{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{H}_{2}}}=\sqrt{\frac{\frac{1}{\frac{32}{1}}}{\frac{1}{2}}}=\frac{1}{4}$ $\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}=\frac{\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}{4}=\frac{\mathrm{C}}{4}$
WB JEE 2016
Kinetic Theory of Gases
139263
At what temperature will be rms speed of air molecules be double that of NTP?
139264
Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units respectively. The rms speed is
1 4 units
2 1.7 units
3 4.2 units
4 5 units
Explanation:
C Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{v}_{1}^{2}+\mathrm{v}_{2}^{2}+\ldots \ldots .+\mathrm{v}_{\mathrm{n}}^{2}}{\mathrm{n}}}$ $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{4+25+9+36+9+25}{6}}=\sqrt{\frac{108}{6}}=\sqrt{18}=3 \sqrt{2}$ $\mathrm{v}_{\mathrm{rms}}=3 \times 1.414=4.242$ units
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Kinetic Theory of Gases
139249
The root-mean- square speed and average kinetic energy of the molecules of an ideal gas at absolute temperature $T$ are respectively proportional to
1 $\mathrm{T}$ and $\mathrm{T}^{-1}$
2 $\sqrt{\mathrm{T}}$ and $\mathrm{T}$
3 $\mathrm{T}$ and $\mathrm{T}^{2}$
4 $\mathrm{T}^{-1}$ and $\mathrm{T}$
Explanation:
B The root mean square speed of molecule is given as, $\mathrm{v}_{\text {rms }}=\sqrt{\frac{3 R T}{M}}$ $\mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$ Average kinetic energy (K.E.) $=\frac{3}{2} \mathrm{KT}$ $\therefore \quad$ K.E. $\propto \mathrm{T}$
SCRA-2013
Kinetic Theory of Gases
139255
The average energy per molecule of a triatomic gas at room temperature $T$ is
1 $3 \mathrm{kT}$
2 $\frac{1}{2} \mathrm{kT}$
3 $\frac{3}{2} \mathrm{kT}$
4 $\frac{5}{2} \mathrm{kT}$
Explanation:
A At room temperature $\mathrm{T}$ the degrees of freedom of triatomic gas $\mathrm{f}=6$ (3rotatonal, 3translation) So, $\text { Energy }=\frac{f}{2} K T$ $E=\frac{6}{2} K T=3 K T$
J and K-CET-2016
Kinetic Theory of Gases
139260
If the rms velocity of hydrogen gas at a certain temperature is $c$, then the rms velocity of oxygen gas at the same temperature is
1 $\frac{\mathrm{c}}{8}$
2 $\frac{\mathrm{c}}{10}$
3 $\frac{\mathrm{c}}{4}$
4 $\frac{\mathrm{c}}{2}$
Explanation:
C Molar mass of oxygen $=32$ Molar mass of Hydrogen $=2$ RMS velocity $\left(\mathrm{v}_{\mathrm{rms}}\right)=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{1}{\mathrm{M}}}$ Now, $\frac{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{O}_{2}}}{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{H}_{2}}}=\sqrt{\frac{\frac{1}{\frac{32}{1}}}{\frac{1}{2}}}=\frac{1}{4}$ $\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}=\frac{\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}{4}=\frac{\mathrm{C}}{4}$
WB JEE 2016
Kinetic Theory of Gases
139263
At what temperature will be rms speed of air molecules be double that of NTP?
139264
Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units respectively. The rms speed is
1 4 units
2 1.7 units
3 4.2 units
4 5 units
Explanation:
C Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{v}_{1}^{2}+\mathrm{v}_{2}^{2}+\ldots \ldots .+\mathrm{v}_{\mathrm{n}}^{2}}{\mathrm{n}}}$ $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{4+25+9+36+9+25}{6}}=\sqrt{\frac{108}{6}}=\sqrt{18}=3 \sqrt{2}$ $\mathrm{v}_{\mathrm{rms}}=3 \times 1.414=4.242$ units
139249
The root-mean- square speed and average kinetic energy of the molecules of an ideal gas at absolute temperature $T$ are respectively proportional to
1 $\mathrm{T}$ and $\mathrm{T}^{-1}$
2 $\sqrt{\mathrm{T}}$ and $\mathrm{T}$
3 $\mathrm{T}$ and $\mathrm{T}^{2}$
4 $\mathrm{T}^{-1}$ and $\mathrm{T}$
Explanation:
B The root mean square speed of molecule is given as, $\mathrm{v}_{\text {rms }}=\sqrt{\frac{3 R T}{M}}$ $\mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$ Average kinetic energy (K.E.) $=\frac{3}{2} \mathrm{KT}$ $\therefore \quad$ K.E. $\propto \mathrm{T}$
SCRA-2013
Kinetic Theory of Gases
139255
The average energy per molecule of a triatomic gas at room temperature $T$ is
1 $3 \mathrm{kT}$
2 $\frac{1}{2} \mathrm{kT}$
3 $\frac{3}{2} \mathrm{kT}$
4 $\frac{5}{2} \mathrm{kT}$
Explanation:
A At room temperature $\mathrm{T}$ the degrees of freedom of triatomic gas $\mathrm{f}=6$ (3rotatonal, 3translation) So, $\text { Energy }=\frac{f}{2} K T$ $E=\frac{6}{2} K T=3 K T$
J and K-CET-2016
Kinetic Theory of Gases
139260
If the rms velocity of hydrogen gas at a certain temperature is $c$, then the rms velocity of oxygen gas at the same temperature is
1 $\frac{\mathrm{c}}{8}$
2 $\frac{\mathrm{c}}{10}$
3 $\frac{\mathrm{c}}{4}$
4 $\frac{\mathrm{c}}{2}$
Explanation:
C Molar mass of oxygen $=32$ Molar mass of Hydrogen $=2$ RMS velocity $\left(\mathrm{v}_{\mathrm{rms}}\right)=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{1}{\mathrm{M}}}$ Now, $\frac{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{O}_{2}}}{\left(\mathrm{v}_{\text {rms }}\right)_{\mathrm{H}_{2}}}=\sqrt{\frac{\frac{1}{\frac{32}{1}}}{\frac{1}{2}}}=\frac{1}{4}$ $\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}=\frac{\left(\mathrm{v}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}{4}=\frac{\mathrm{C}}{4}$
WB JEE 2016
Kinetic Theory of Gases
139263
At what temperature will be rms speed of air molecules be double that of NTP?
139264
Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units respectively. The rms speed is
1 4 units
2 1.7 units
3 4.2 units
4 5 units
Explanation:
C Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units and 5 units $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{v}_{1}^{2}+\mathrm{v}_{2}^{2}+\ldots \ldots .+\mathrm{v}_{\mathrm{n}}^{2}}{\mathrm{n}}}$ $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{4+25+9+36+9+25}{6}}=\sqrt{\frac{108}{6}}=\sqrt{18}=3 \sqrt{2}$ $\mathrm{v}_{\mathrm{rms}}=3 \times 1.414=4.242$ units