360200
At what temperature the average speed of \({{O}_{2}}\) will be \({\left(\dfrac{7}{4}\right)^{\text {th }}}\) of rms speed of \({N_{2}}\) at \({47^{\circ} {C}}\) ?
1 \({1320 k}\)
2 \({1600 k}\)
3 \({850 k}\)
4 \({700 k}\)
Explanation:
\({\left(v_{O_{2}}\right)_{a v}=\dfrac{7}{4}\left(v_{r m s}\right)_{N_{2}}}\) \({T_{1}=}\) ?, \({T_{2}=320 {~K}}\) \({\sqrt{\dfrac{8 R T_{1}}{\pi M_{1}}}=\dfrac{7}{4} \sqrt{\dfrac{3 R T_{2}}{M_{2}}}}\) \({\dfrac{8 R T_{1}}{3.14 \times 32}=\dfrac{49 \times 3 R \times 320}{16 \times 28} \Rightarrow T_{1}=1320 K}\)
PHXI13:KINETIC THEORY
360201
The gas having average speed four times as that of \(\mathrm{SO}_{2}\) (molecular mass 64) is
1 \(C{H_4}\) (molecular mass 16)
2 \({O_2}\) (molecular mass 32)
3 \({H_2}\) (molecular mass 2)
4 \(He\) (molecular mass 4 )
Explanation:
As temperature is constant \({v_{av}} \propto \frac{1}{{\sqrt M }} \Rightarrow \frac{{{v_{Gas}}}}{{{v_{S{O_2}}}}} = \sqrt {\frac{{{M_{S{O_2}}}}}{{{M_{Gas}}}}} \Rightarrow \frac{4}{1} = \sqrt {\frac{{64}}{{{M_{Gas}}}}} \) \({M_{Gas}} = 4,i.e.,\,\,gas\,\,is\,\,He.\)
PHXI13:KINETIC THEORY
360202
The respective speeds of five molecules are 2 , \(1.5,1.6,1.6\) and\(1.2\;km{\rm{/sec}}\). The most probable speed in \(km{\rm{/sec}}\) will be
1 2
2 1.58
3 1.6
4 1.31
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3}{2}} V_{m p}\) \(\Rightarrow V_{m p}=\sqrt{\dfrac{2}{3}} V_{r m s}\) \(V_{r m s}=\sqrt{\dfrac{4+2.25+2.56+2.56+1.44}{5}}=\sqrt{2.562}\) \( \Rightarrow {V_{mp}} = \sqrt {\frac{2}{3} \times 2.562} = \sqrt {1.708} = 1.30\;km{\rm{/}}s\) \( \approx 1.31\,\)So correct option is (4).
PHXI13:KINETIC THEORY
360203
Assertion : The root mean square and most probable speeds of the molecules in a gas are the same. Reason : The maxwell distribution for the speed of molecules in a gas is symmetrical.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
360200
At what temperature the average speed of \({{O}_{2}}\) will be \({\left(\dfrac{7}{4}\right)^{\text {th }}}\) of rms speed of \({N_{2}}\) at \({47^{\circ} {C}}\) ?
1 \({1320 k}\)
2 \({1600 k}\)
3 \({850 k}\)
4 \({700 k}\)
Explanation:
\({\left(v_{O_{2}}\right)_{a v}=\dfrac{7}{4}\left(v_{r m s}\right)_{N_{2}}}\) \({T_{1}=}\) ?, \({T_{2}=320 {~K}}\) \({\sqrt{\dfrac{8 R T_{1}}{\pi M_{1}}}=\dfrac{7}{4} \sqrt{\dfrac{3 R T_{2}}{M_{2}}}}\) \({\dfrac{8 R T_{1}}{3.14 \times 32}=\dfrac{49 \times 3 R \times 320}{16 \times 28} \Rightarrow T_{1}=1320 K}\)
PHXI13:KINETIC THEORY
360201
The gas having average speed four times as that of \(\mathrm{SO}_{2}\) (molecular mass 64) is
1 \(C{H_4}\) (molecular mass 16)
2 \({O_2}\) (molecular mass 32)
3 \({H_2}\) (molecular mass 2)
4 \(He\) (molecular mass 4 )
Explanation:
As temperature is constant \({v_{av}} \propto \frac{1}{{\sqrt M }} \Rightarrow \frac{{{v_{Gas}}}}{{{v_{S{O_2}}}}} = \sqrt {\frac{{{M_{S{O_2}}}}}{{{M_{Gas}}}}} \Rightarrow \frac{4}{1} = \sqrt {\frac{{64}}{{{M_{Gas}}}}} \) \({M_{Gas}} = 4,i.e.,\,\,gas\,\,is\,\,He.\)
PHXI13:KINETIC THEORY
360202
The respective speeds of five molecules are 2 , \(1.5,1.6,1.6\) and\(1.2\;km{\rm{/sec}}\). The most probable speed in \(km{\rm{/sec}}\) will be
1 2
2 1.58
3 1.6
4 1.31
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3}{2}} V_{m p}\) \(\Rightarrow V_{m p}=\sqrt{\dfrac{2}{3}} V_{r m s}\) \(V_{r m s}=\sqrt{\dfrac{4+2.25+2.56+2.56+1.44}{5}}=\sqrt{2.562}\) \( \Rightarrow {V_{mp}} = \sqrt {\frac{2}{3} \times 2.562} = \sqrt {1.708} = 1.30\;km{\rm{/}}s\) \( \approx 1.31\,\)So correct option is (4).
PHXI13:KINETIC THEORY
360203
Assertion : The root mean square and most probable speeds of the molecules in a gas are the same. Reason : The maxwell distribution for the speed of molecules in a gas is symmetrical.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
360200
At what temperature the average speed of \({{O}_{2}}\) will be \({\left(\dfrac{7}{4}\right)^{\text {th }}}\) of rms speed of \({N_{2}}\) at \({47^{\circ} {C}}\) ?
1 \({1320 k}\)
2 \({1600 k}\)
3 \({850 k}\)
4 \({700 k}\)
Explanation:
\({\left(v_{O_{2}}\right)_{a v}=\dfrac{7}{4}\left(v_{r m s}\right)_{N_{2}}}\) \({T_{1}=}\) ?, \({T_{2}=320 {~K}}\) \({\sqrt{\dfrac{8 R T_{1}}{\pi M_{1}}}=\dfrac{7}{4} \sqrt{\dfrac{3 R T_{2}}{M_{2}}}}\) \({\dfrac{8 R T_{1}}{3.14 \times 32}=\dfrac{49 \times 3 R \times 320}{16 \times 28} \Rightarrow T_{1}=1320 K}\)
PHXI13:KINETIC THEORY
360201
The gas having average speed four times as that of \(\mathrm{SO}_{2}\) (molecular mass 64) is
1 \(C{H_4}\) (molecular mass 16)
2 \({O_2}\) (molecular mass 32)
3 \({H_2}\) (molecular mass 2)
4 \(He\) (molecular mass 4 )
Explanation:
As temperature is constant \({v_{av}} \propto \frac{1}{{\sqrt M }} \Rightarrow \frac{{{v_{Gas}}}}{{{v_{S{O_2}}}}} = \sqrt {\frac{{{M_{S{O_2}}}}}{{{M_{Gas}}}}} \Rightarrow \frac{4}{1} = \sqrt {\frac{{64}}{{{M_{Gas}}}}} \) \({M_{Gas}} = 4,i.e.,\,\,gas\,\,is\,\,He.\)
PHXI13:KINETIC THEORY
360202
The respective speeds of five molecules are 2 , \(1.5,1.6,1.6\) and\(1.2\;km{\rm{/sec}}\). The most probable speed in \(km{\rm{/sec}}\) will be
1 2
2 1.58
3 1.6
4 1.31
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3}{2}} V_{m p}\) \(\Rightarrow V_{m p}=\sqrt{\dfrac{2}{3}} V_{r m s}\) \(V_{r m s}=\sqrt{\dfrac{4+2.25+2.56+2.56+1.44}{5}}=\sqrt{2.562}\) \( \Rightarrow {V_{mp}} = \sqrt {\frac{2}{3} \times 2.562} = \sqrt {1.708} = 1.30\;km{\rm{/}}s\) \( \approx 1.31\,\)So correct option is (4).
PHXI13:KINETIC THEORY
360203
Assertion : The root mean square and most probable speeds of the molecules in a gas are the same. Reason : The maxwell distribution for the speed of molecules in a gas is symmetrical.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
360200
At what temperature the average speed of \({{O}_{2}}\) will be \({\left(\dfrac{7}{4}\right)^{\text {th }}}\) of rms speed of \({N_{2}}\) at \({47^{\circ} {C}}\) ?
1 \({1320 k}\)
2 \({1600 k}\)
3 \({850 k}\)
4 \({700 k}\)
Explanation:
\({\left(v_{O_{2}}\right)_{a v}=\dfrac{7}{4}\left(v_{r m s}\right)_{N_{2}}}\) \({T_{1}=}\) ?, \({T_{2}=320 {~K}}\) \({\sqrt{\dfrac{8 R T_{1}}{\pi M_{1}}}=\dfrac{7}{4} \sqrt{\dfrac{3 R T_{2}}{M_{2}}}}\) \({\dfrac{8 R T_{1}}{3.14 \times 32}=\dfrac{49 \times 3 R \times 320}{16 \times 28} \Rightarrow T_{1}=1320 K}\)
PHXI13:KINETIC THEORY
360201
The gas having average speed four times as that of \(\mathrm{SO}_{2}\) (molecular mass 64) is
1 \(C{H_4}\) (molecular mass 16)
2 \({O_2}\) (molecular mass 32)
3 \({H_2}\) (molecular mass 2)
4 \(He\) (molecular mass 4 )
Explanation:
As temperature is constant \({v_{av}} \propto \frac{1}{{\sqrt M }} \Rightarrow \frac{{{v_{Gas}}}}{{{v_{S{O_2}}}}} = \sqrt {\frac{{{M_{S{O_2}}}}}{{{M_{Gas}}}}} \Rightarrow \frac{4}{1} = \sqrt {\frac{{64}}{{{M_{Gas}}}}} \) \({M_{Gas}} = 4,i.e.,\,\,gas\,\,is\,\,He.\)
PHXI13:KINETIC THEORY
360202
The respective speeds of five molecules are 2 , \(1.5,1.6,1.6\) and\(1.2\;km{\rm{/sec}}\). The most probable speed in \(km{\rm{/sec}}\) will be
1 2
2 1.58
3 1.6
4 1.31
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3}{2}} V_{m p}\) \(\Rightarrow V_{m p}=\sqrt{\dfrac{2}{3}} V_{r m s}\) \(V_{r m s}=\sqrt{\dfrac{4+2.25+2.56+2.56+1.44}{5}}=\sqrt{2.562}\) \( \Rightarrow {V_{mp}} = \sqrt {\frac{2}{3} \times 2.562} = \sqrt {1.708} = 1.30\;km{\rm{/}}s\) \( \approx 1.31\,\)So correct option is (4).
PHXI13:KINETIC THEORY
360203
Assertion : The root mean square and most probable speeds of the molecules in a gas are the same. Reason : The maxwell distribution for the speed of molecules in a gas is symmetrical.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
