360195
Statement A : The ratio of rms speed and average speed of a gas molecules at a given temperature is \(\sqrt{3}: \sqrt{2}\) Statement B : \(c_{r m s} < c_{a v}\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(c_{r m s}=\sqrt{\dfrac{3 k T}{m}}\) and \({c_{avg{\rm{ }}}} = \sqrt {\frac{{8kT}}{{\pi m}}} \) \(\therefore \dfrac{c_{r m s}}{c_{\text {avg }}}=\dfrac{\sqrt{3}}{(\sqrt{8 / \pi})}>1\) Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360196
The molecules in an ideal gas at \(27^\circ C\) have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled
1 \(54^\circ C\)
2 \(927^\circ C\)
3 \(1200^\circ C\)
4 \(327^\circ C\)
Explanation:
Mean velocity of gas molecules is, \(v=\sqrt{\dfrac{8 R T}{\pi M}}\) where, \(T = \) Temperature of the gas in kelvin \(M = \) Molar mass, \(R = \) Universal gas constant For the same gas, \(v \propto \sqrt{T}\) \(\therefore \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}}}=\sqrt{\dfrac{300}{T_{2}}} \Rightarrow \dfrac{v_{1}}{2 v_{1}}=\sqrt{\dfrac{300}{T_{2}}}\) Squaring both sides, we get, \(\dfrac{1}{4}=\dfrac{300}{T_{2}}\) \({T_2} = 1200\,\,K = 1200 - 273 = 927^\circ C\)
PHXI13:KINETIC THEORY
360197
A vessel of volume \(V\) contains a mixture of 1 mole of hydrogen and 1 mole of oxygen (both considered as ideal). Let \(f_{1}(v) d v\), denote the function for molecules of \({H_2}\) with speed between \(v\) and \((v+d v)\) and \(f_{2}(v) d v\) for oxygen. Then
1 \(f_{2}(v)+f_{2}(v)=f(v)\) obeys the Maxwell's distribution law
2 \(f_{1}(v), f_{2}(v)\) will obey the Maxwell's distribution law
3 Neither \(f_{1}(v)\), nor \(f_{2}(v)\) will obey the Maxwell's distribution law
4 \(f_{2}(v)\) and \(f_{1}(v)\) will be the same
Explanation:
As the vessel contains both hydrogen and oxygen, therfore, as per Maxwell's law of speed distribution, \(f_{1}(v)\) and \(f_{2}(v)\) will obey the law separately. (In general \(f(v)=\) constant \(\times v^{2} e^{-\left(m v^{2} / 2 K T\right)}\) Where \(m = \) mass of one molecule)
NCERT Exemplar
PHXI13:KINETIC THEORY
360198
For a gas at a temperature \(\mathrm{T}\) the root-meansquare velocity \(v_{r m s}\), the most probable speed \(v_{m p}\), and the average speed \(v_{a v}\) obey the relationship
1 \(v_{m p}>v_{a v}>v_{r m s}\)
2 \(v_{r m s}>v_{a v}>v_{m p}\)
3 \(v_{m p}>v_{r m s}>v_{a v}\)
4 \(v_{a v}>v_{r m s}>v_{m p}\)
Explanation:
\(v_{r m s}>v_{a v}>v_{m p}\), \(v_{r m s}=\sqrt{\dfrac{3 R T}{M}}, v_{m p}=\sqrt{\dfrac{2 R T}{M}}\) and \(v_{a v}=\sqrt{\dfrac{8 R T}{\pi M}}\)
PHXI13:KINETIC THEORY
360199
For an ideal gas a graph is drawn between number of molecules at a particular speed \(\left(\dfrac{d N}{d v}\right)\) and speed of the molecules \((v)\). Predict the correct option.
1 Point A represents the most probable speed \(\left(v_{m p}\right)\)
2 The area under the graph represents total number of molecules
3 Number of molecules having speed less than \(v_{m p}\) is less than the number of molecules having speeds more than \(v_{m p}\)
4 All the above
Explanation:
The maximum value of \(\dfrac{d N}{d v}\) represents most probable speed of gas particles. Area of the graph is \(A=\int \dfrac{d N}{d v} d v=\) Total no of particles. It is always true that area of the graph on the right side of \(v_{m p}\) is more than the area on the left side of \(v_{m p}\).
360195
Statement A : The ratio of rms speed and average speed of a gas molecules at a given temperature is \(\sqrt{3}: \sqrt{2}\) Statement B : \(c_{r m s} < c_{a v}\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(c_{r m s}=\sqrt{\dfrac{3 k T}{m}}\) and \({c_{avg{\rm{ }}}} = \sqrt {\frac{{8kT}}{{\pi m}}} \) \(\therefore \dfrac{c_{r m s}}{c_{\text {avg }}}=\dfrac{\sqrt{3}}{(\sqrt{8 / \pi})}>1\) Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360196
The molecules in an ideal gas at \(27^\circ C\) have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled
1 \(54^\circ C\)
2 \(927^\circ C\)
3 \(1200^\circ C\)
4 \(327^\circ C\)
Explanation:
Mean velocity of gas molecules is, \(v=\sqrt{\dfrac{8 R T}{\pi M}}\) where, \(T = \) Temperature of the gas in kelvin \(M = \) Molar mass, \(R = \) Universal gas constant For the same gas, \(v \propto \sqrt{T}\) \(\therefore \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}}}=\sqrt{\dfrac{300}{T_{2}}} \Rightarrow \dfrac{v_{1}}{2 v_{1}}=\sqrt{\dfrac{300}{T_{2}}}\) Squaring both sides, we get, \(\dfrac{1}{4}=\dfrac{300}{T_{2}}\) \({T_2} = 1200\,\,K = 1200 - 273 = 927^\circ C\)
PHXI13:KINETIC THEORY
360197
A vessel of volume \(V\) contains a mixture of 1 mole of hydrogen and 1 mole of oxygen (both considered as ideal). Let \(f_{1}(v) d v\), denote the function for molecules of \({H_2}\) with speed between \(v\) and \((v+d v)\) and \(f_{2}(v) d v\) for oxygen. Then
1 \(f_{2}(v)+f_{2}(v)=f(v)\) obeys the Maxwell's distribution law
2 \(f_{1}(v), f_{2}(v)\) will obey the Maxwell's distribution law
3 Neither \(f_{1}(v)\), nor \(f_{2}(v)\) will obey the Maxwell's distribution law
4 \(f_{2}(v)\) and \(f_{1}(v)\) will be the same
Explanation:
As the vessel contains both hydrogen and oxygen, therfore, as per Maxwell's law of speed distribution, \(f_{1}(v)\) and \(f_{2}(v)\) will obey the law separately. (In general \(f(v)=\) constant \(\times v^{2} e^{-\left(m v^{2} / 2 K T\right)}\) Where \(m = \) mass of one molecule)
NCERT Exemplar
PHXI13:KINETIC THEORY
360198
For a gas at a temperature \(\mathrm{T}\) the root-meansquare velocity \(v_{r m s}\), the most probable speed \(v_{m p}\), and the average speed \(v_{a v}\) obey the relationship
1 \(v_{m p}>v_{a v}>v_{r m s}\)
2 \(v_{r m s}>v_{a v}>v_{m p}\)
3 \(v_{m p}>v_{r m s}>v_{a v}\)
4 \(v_{a v}>v_{r m s}>v_{m p}\)
Explanation:
\(v_{r m s}>v_{a v}>v_{m p}\), \(v_{r m s}=\sqrt{\dfrac{3 R T}{M}}, v_{m p}=\sqrt{\dfrac{2 R T}{M}}\) and \(v_{a v}=\sqrt{\dfrac{8 R T}{\pi M}}\)
PHXI13:KINETIC THEORY
360199
For an ideal gas a graph is drawn between number of molecules at a particular speed \(\left(\dfrac{d N}{d v}\right)\) and speed of the molecules \((v)\). Predict the correct option.
1 Point A represents the most probable speed \(\left(v_{m p}\right)\)
2 The area under the graph represents total number of molecules
3 Number of molecules having speed less than \(v_{m p}\) is less than the number of molecules having speeds more than \(v_{m p}\)
4 All the above
Explanation:
The maximum value of \(\dfrac{d N}{d v}\) represents most probable speed of gas particles. Area of the graph is \(A=\int \dfrac{d N}{d v} d v=\) Total no of particles. It is always true that area of the graph on the right side of \(v_{m p}\) is more than the area on the left side of \(v_{m p}\).
360195
Statement A : The ratio of rms speed and average speed of a gas molecules at a given temperature is \(\sqrt{3}: \sqrt{2}\) Statement B : \(c_{r m s} < c_{a v}\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(c_{r m s}=\sqrt{\dfrac{3 k T}{m}}\) and \({c_{avg{\rm{ }}}} = \sqrt {\frac{{8kT}}{{\pi m}}} \) \(\therefore \dfrac{c_{r m s}}{c_{\text {avg }}}=\dfrac{\sqrt{3}}{(\sqrt{8 / \pi})}>1\) Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360196
The molecules in an ideal gas at \(27^\circ C\) have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled
1 \(54^\circ C\)
2 \(927^\circ C\)
3 \(1200^\circ C\)
4 \(327^\circ C\)
Explanation:
Mean velocity of gas molecules is, \(v=\sqrt{\dfrac{8 R T}{\pi M}}\) where, \(T = \) Temperature of the gas in kelvin \(M = \) Molar mass, \(R = \) Universal gas constant For the same gas, \(v \propto \sqrt{T}\) \(\therefore \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}}}=\sqrt{\dfrac{300}{T_{2}}} \Rightarrow \dfrac{v_{1}}{2 v_{1}}=\sqrt{\dfrac{300}{T_{2}}}\) Squaring both sides, we get, \(\dfrac{1}{4}=\dfrac{300}{T_{2}}\) \({T_2} = 1200\,\,K = 1200 - 273 = 927^\circ C\)
PHXI13:KINETIC THEORY
360197
A vessel of volume \(V\) contains a mixture of 1 mole of hydrogen and 1 mole of oxygen (both considered as ideal). Let \(f_{1}(v) d v\), denote the function for molecules of \({H_2}\) with speed between \(v\) and \((v+d v)\) and \(f_{2}(v) d v\) for oxygen. Then
1 \(f_{2}(v)+f_{2}(v)=f(v)\) obeys the Maxwell's distribution law
2 \(f_{1}(v), f_{2}(v)\) will obey the Maxwell's distribution law
3 Neither \(f_{1}(v)\), nor \(f_{2}(v)\) will obey the Maxwell's distribution law
4 \(f_{2}(v)\) and \(f_{1}(v)\) will be the same
Explanation:
As the vessel contains both hydrogen and oxygen, therfore, as per Maxwell's law of speed distribution, \(f_{1}(v)\) and \(f_{2}(v)\) will obey the law separately. (In general \(f(v)=\) constant \(\times v^{2} e^{-\left(m v^{2} / 2 K T\right)}\) Where \(m = \) mass of one molecule)
NCERT Exemplar
PHXI13:KINETIC THEORY
360198
For a gas at a temperature \(\mathrm{T}\) the root-meansquare velocity \(v_{r m s}\), the most probable speed \(v_{m p}\), and the average speed \(v_{a v}\) obey the relationship
1 \(v_{m p}>v_{a v}>v_{r m s}\)
2 \(v_{r m s}>v_{a v}>v_{m p}\)
3 \(v_{m p}>v_{r m s}>v_{a v}\)
4 \(v_{a v}>v_{r m s}>v_{m p}\)
Explanation:
\(v_{r m s}>v_{a v}>v_{m p}\), \(v_{r m s}=\sqrt{\dfrac{3 R T}{M}}, v_{m p}=\sqrt{\dfrac{2 R T}{M}}\) and \(v_{a v}=\sqrt{\dfrac{8 R T}{\pi M}}\)
PHXI13:KINETIC THEORY
360199
For an ideal gas a graph is drawn between number of molecules at a particular speed \(\left(\dfrac{d N}{d v}\right)\) and speed of the molecules \((v)\). Predict the correct option.
1 Point A represents the most probable speed \(\left(v_{m p}\right)\)
2 The area under the graph represents total number of molecules
3 Number of molecules having speed less than \(v_{m p}\) is less than the number of molecules having speeds more than \(v_{m p}\)
4 All the above
Explanation:
The maximum value of \(\dfrac{d N}{d v}\) represents most probable speed of gas particles. Area of the graph is \(A=\int \dfrac{d N}{d v} d v=\) Total no of particles. It is always true that area of the graph on the right side of \(v_{m p}\) is more than the area on the left side of \(v_{m p}\).
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI13:KINETIC THEORY
360195
Statement A : The ratio of rms speed and average speed of a gas molecules at a given temperature is \(\sqrt{3}: \sqrt{2}\) Statement B : \(c_{r m s} < c_{a v}\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(c_{r m s}=\sqrt{\dfrac{3 k T}{m}}\) and \({c_{avg{\rm{ }}}} = \sqrt {\frac{{8kT}}{{\pi m}}} \) \(\therefore \dfrac{c_{r m s}}{c_{\text {avg }}}=\dfrac{\sqrt{3}}{(\sqrt{8 / \pi})}>1\) Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360196
The molecules in an ideal gas at \(27^\circ C\) have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled
1 \(54^\circ C\)
2 \(927^\circ C\)
3 \(1200^\circ C\)
4 \(327^\circ C\)
Explanation:
Mean velocity of gas molecules is, \(v=\sqrt{\dfrac{8 R T}{\pi M}}\) where, \(T = \) Temperature of the gas in kelvin \(M = \) Molar mass, \(R = \) Universal gas constant For the same gas, \(v \propto \sqrt{T}\) \(\therefore \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}}}=\sqrt{\dfrac{300}{T_{2}}} \Rightarrow \dfrac{v_{1}}{2 v_{1}}=\sqrt{\dfrac{300}{T_{2}}}\) Squaring both sides, we get, \(\dfrac{1}{4}=\dfrac{300}{T_{2}}\) \({T_2} = 1200\,\,K = 1200 - 273 = 927^\circ C\)
PHXI13:KINETIC THEORY
360197
A vessel of volume \(V\) contains a mixture of 1 mole of hydrogen and 1 mole of oxygen (both considered as ideal). Let \(f_{1}(v) d v\), denote the function for molecules of \({H_2}\) with speed between \(v\) and \((v+d v)\) and \(f_{2}(v) d v\) for oxygen. Then
1 \(f_{2}(v)+f_{2}(v)=f(v)\) obeys the Maxwell's distribution law
2 \(f_{1}(v), f_{2}(v)\) will obey the Maxwell's distribution law
3 Neither \(f_{1}(v)\), nor \(f_{2}(v)\) will obey the Maxwell's distribution law
4 \(f_{2}(v)\) and \(f_{1}(v)\) will be the same
Explanation:
As the vessel contains both hydrogen and oxygen, therfore, as per Maxwell's law of speed distribution, \(f_{1}(v)\) and \(f_{2}(v)\) will obey the law separately. (In general \(f(v)=\) constant \(\times v^{2} e^{-\left(m v^{2} / 2 K T\right)}\) Where \(m = \) mass of one molecule)
NCERT Exemplar
PHXI13:KINETIC THEORY
360198
For a gas at a temperature \(\mathrm{T}\) the root-meansquare velocity \(v_{r m s}\), the most probable speed \(v_{m p}\), and the average speed \(v_{a v}\) obey the relationship
1 \(v_{m p}>v_{a v}>v_{r m s}\)
2 \(v_{r m s}>v_{a v}>v_{m p}\)
3 \(v_{m p}>v_{r m s}>v_{a v}\)
4 \(v_{a v}>v_{r m s}>v_{m p}\)
Explanation:
\(v_{r m s}>v_{a v}>v_{m p}\), \(v_{r m s}=\sqrt{\dfrac{3 R T}{M}}, v_{m p}=\sqrt{\dfrac{2 R T}{M}}\) and \(v_{a v}=\sqrt{\dfrac{8 R T}{\pi M}}\)
PHXI13:KINETIC THEORY
360199
For an ideal gas a graph is drawn between number of molecules at a particular speed \(\left(\dfrac{d N}{d v}\right)\) and speed of the molecules \((v)\). Predict the correct option.
1 Point A represents the most probable speed \(\left(v_{m p}\right)\)
2 The area under the graph represents total number of molecules
3 Number of molecules having speed less than \(v_{m p}\) is less than the number of molecules having speeds more than \(v_{m p}\)
4 All the above
Explanation:
The maximum value of \(\dfrac{d N}{d v}\) represents most probable speed of gas particles. Area of the graph is \(A=\int \dfrac{d N}{d v} d v=\) Total no of particles. It is always true that area of the graph on the right side of \(v_{m p}\) is more than the area on the left side of \(v_{m p}\).
360195
Statement A : The ratio of rms speed and average speed of a gas molecules at a given temperature is \(\sqrt{3}: \sqrt{2}\) Statement B : \(c_{r m s} < c_{a v}\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
\(c_{r m s}=\sqrt{\dfrac{3 k T}{m}}\) and \({c_{avg{\rm{ }}}} = \sqrt {\frac{{8kT}}{{\pi m}}} \) \(\therefore \dfrac{c_{r m s}}{c_{\text {avg }}}=\dfrac{\sqrt{3}}{(\sqrt{8 / \pi})}>1\) Both statements are wrong. So option (4) is correct.
PHXI13:KINETIC THEORY
360196
The molecules in an ideal gas at \(27^\circ C\) have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled
1 \(54^\circ C\)
2 \(927^\circ C\)
3 \(1200^\circ C\)
4 \(327^\circ C\)
Explanation:
Mean velocity of gas molecules is, \(v=\sqrt{\dfrac{8 R T}{\pi M}}\) where, \(T = \) Temperature of the gas in kelvin \(M = \) Molar mass, \(R = \) Universal gas constant For the same gas, \(v \propto \sqrt{T}\) \(\therefore \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}}}=\sqrt{\dfrac{300}{T_{2}}} \Rightarrow \dfrac{v_{1}}{2 v_{1}}=\sqrt{\dfrac{300}{T_{2}}}\) Squaring both sides, we get, \(\dfrac{1}{4}=\dfrac{300}{T_{2}}\) \({T_2} = 1200\,\,K = 1200 - 273 = 927^\circ C\)
PHXI13:KINETIC THEORY
360197
A vessel of volume \(V\) contains a mixture of 1 mole of hydrogen and 1 mole of oxygen (both considered as ideal). Let \(f_{1}(v) d v\), denote the function for molecules of \({H_2}\) with speed between \(v\) and \((v+d v)\) and \(f_{2}(v) d v\) for oxygen. Then
1 \(f_{2}(v)+f_{2}(v)=f(v)\) obeys the Maxwell's distribution law
2 \(f_{1}(v), f_{2}(v)\) will obey the Maxwell's distribution law
3 Neither \(f_{1}(v)\), nor \(f_{2}(v)\) will obey the Maxwell's distribution law
4 \(f_{2}(v)\) and \(f_{1}(v)\) will be the same
Explanation:
As the vessel contains both hydrogen and oxygen, therfore, as per Maxwell's law of speed distribution, \(f_{1}(v)\) and \(f_{2}(v)\) will obey the law separately. (In general \(f(v)=\) constant \(\times v^{2} e^{-\left(m v^{2} / 2 K T\right)}\) Where \(m = \) mass of one molecule)
NCERT Exemplar
PHXI13:KINETIC THEORY
360198
For a gas at a temperature \(\mathrm{T}\) the root-meansquare velocity \(v_{r m s}\), the most probable speed \(v_{m p}\), and the average speed \(v_{a v}\) obey the relationship
1 \(v_{m p}>v_{a v}>v_{r m s}\)
2 \(v_{r m s}>v_{a v}>v_{m p}\)
3 \(v_{m p}>v_{r m s}>v_{a v}\)
4 \(v_{a v}>v_{r m s}>v_{m p}\)
Explanation:
\(v_{r m s}>v_{a v}>v_{m p}\), \(v_{r m s}=\sqrt{\dfrac{3 R T}{M}}, v_{m p}=\sqrt{\dfrac{2 R T}{M}}\) and \(v_{a v}=\sqrt{\dfrac{8 R T}{\pi M}}\)
PHXI13:KINETIC THEORY
360199
For an ideal gas a graph is drawn between number of molecules at a particular speed \(\left(\dfrac{d N}{d v}\right)\) and speed of the molecules \((v)\). Predict the correct option.
1 Point A represents the most probable speed \(\left(v_{m p}\right)\)
2 The area under the graph represents total number of molecules
3 Number of molecules having speed less than \(v_{m p}\) is less than the number of molecules having speeds more than \(v_{m p}\)
4 All the above
Explanation:
The maximum value of \(\dfrac{d N}{d v}\) represents most probable speed of gas particles. Area of the graph is \(A=\int \dfrac{d N}{d v} d v=\) Total no of particles. It is always true that area of the graph on the right side of \(v_{m p}\) is more than the area on the left side of \(v_{m p}\).
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