360238
A mixture of two gases is contained in a vessel. The gas-I is monoatomic and gas-II is diatomic. The ratio of their molecular weights is \(1: 4\). The ratio of R.M.S. speeds of molecules of two gases will be
360239
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is
1 \({\dfrac{1}{32}}\)
2 \({\dfrac{1}{2 \sqrt{2}}}\)
3 \({\dfrac{1}{4}}\)
4 \({\dfrac{2 \sqrt{2}}{1}}\)
Explanation:
We know that, \({M_{O_{2}}=32, M_{H e}=4}\) \({R M S}\) velocity of a gas is given by \({v_{r m s}=\sqrt{\dfrac{3 R T}{M}} \Rightarrow v_{r m s} \propto \dfrac{1}{\sqrt{m}}}\) \({\Rightarrow \dfrac{v_{{He}}}{v_{O_{2}}}=\sqrt{\dfrac{M_{O_{2}}}{M_{{He}}}}=\sqrt{\dfrac{32}{4}}=\dfrac{2 \sqrt{2}}{1}}\) So, correct option is (4).
JEE - 2024
PHXI13:KINETIC THEORY
360240
The r.m.s velocity of a gas at a certain temperature is \(\sqrt{2}\) times than that of the oxygen molecules at that temperature. The gas can be:
1 \({H_2}\)
2 \(He\)
3 \(C{H_4}\)
4 \(S{O_2}\)
Explanation:
\(\quad v_{r m s} \propto \dfrac{1}{\sqrt{M}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{M_{2}}{M_{1}}}\) \(\Rightarrow \dfrac{v}{\sqrt{2} v}=\sqrt{\dfrac{M_{2}}{32}} \Rightarrow M_{2}=16\) So the given gas is \(C{H_4}\)
PHXI13:KINETIC THEORY
360241
At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at \(200 K\) ?
1 \(527^\circ C\)
2 \(1327^\circ C\)
3 \(2127^\circ C\)
4 \(2927^\circ C\)
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3 K T}{M}} \Rightarrow T \propto M\) \(\Rightarrow \dfrac{T_{1}}{T_{2}}=\dfrac{2}{32}\) \(\Rightarrow T_{2}=16 T_{1}=3200 \mathrm{~K}\) \( = 2927^\circ C\).
PHXI13:KINETIC THEORY
360242
Assertion : The rms velocity of gas molecules is doubled, when temperature of gas becomes four times. Reason : \(c \propto \sqrt{T}\).
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.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rms velocity of gas molecules is given by \(v_{\text {rms }}=c=\sqrt{\dfrac{3 k T}{m}}\) Hence, it is clear that when temperature becomes four times rms velocity will be two times.
360238
A mixture of two gases is contained in a vessel. The gas-I is monoatomic and gas-II is diatomic. The ratio of their molecular weights is \(1: 4\). The ratio of R.M.S. speeds of molecules of two gases will be
360239
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is
1 \({\dfrac{1}{32}}\)
2 \({\dfrac{1}{2 \sqrt{2}}}\)
3 \({\dfrac{1}{4}}\)
4 \({\dfrac{2 \sqrt{2}}{1}}\)
Explanation:
We know that, \({M_{O_{2}}=32, M_{H e}=4}\) \({R M S}\) velocity of a gas is given by \({v_{r m s}=\sqrt{\dfrac{3 R T}{M}} \Rightarrow v_{r m s} \propto \dfrac{1}{\sqrt{m}}}\) \({\Rightarrow \dfrac{v_{{He}}}{v_{O_{2}}}=\sqrt{\dfrac{M_{O_{2}}}{M_{{He}}}}=\sqrt{\dfrac{32}{4}}=\dfrac{2 \sqrt{2}}{1}}\) So, correct option is (4).
JEE - 2024
PHXI13:KINETIC THEORY
360240
The r.m.s velocity of a gas at a certain temperature is \(\sqrt{2}\) times than that of the oxygen molecules at that temperature. The gas can be:
1 \({H_2}\)
2 \(He\)
3 \(C{H_4}\)
4 \(S{O_2}\)
Explanation:
\(\quad v_{r m s} \propto \dfrac{1}{\sqrt{M}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{M_{2}}{M_{1}}}\) \(\Rightarrow \dfrac{v}{\sqrt{2} v}=\sqrt{\dfrac{M_{2}}{32}} \Rightarrow M_{2}=16\) So the given gas is \(C{H_4}\)
PHXI13:KINETIC THEORY
360241
At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at \(200 K\) ?
1 \(527^\circ C\)
2 \(1327^\circ C\)
3 \(2127^\circ C\)
4 \(2927^\circ C\)
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3 K T}{M}} \Rightarrow T \propto M\) \(\Rightarrow \dfrac{T_{1}}{T_{2}}=\dfrac{2}{32}\) \(\Rightarrow T_{2}=16 T_{1}=3200 \mathrm{~K}\) \( = 2927^\circ C\).
PHXI13:KINETIC THEORY
360242
Assertion : The rms velocity of gas molecules is doubled, when temperature of gas becomes four times. Reason : \(c \propto \sqrt{T}\).
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.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rms velocity of gas molecules is given by \(v_{\text {rms }}=c=\sqrt{\dfrac{3 k T}{m}}\) Hence, it is clear that when temperature becomes four times rms velocity will be two times.
360238
A mixture of two gases is contained in a vessel. The gas-I is monoatomic and gas-II is diatomic. The ratio of their molecular weights is \(1: 4\). The ratio of R.M.S. speeds of molecules of two gases will be
360239
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is
1 \({\dfrac{1}{32}}\)
2 \({\dfrac{1}{2 \sqrt{2}}}\)
3 \({\dfrac{1}{4}}\)
4 \({\dfrac{2 \sqrt{2}}{1}}\)
Explanation:
We know that, \({M_{O_{2}}=32, M_{H e}=4}\) \({R M S}\) velocity of a gas is given by \({v_{r m s}=\sqrt{\dfrac{3 R T}{M}} \Rightarrow v_{r m s} \propto \dfrac{1}{\sqrt{m}}}\) \({\Rightarrow \dfrac{v_{{He}}}{v_{O_{2}}}=\sqrt{\dfrac{M_{O_{2}}}{M_{{He}}}}=\sqrt{\dfrac{32}{4}}=\dfrac{2 \sqrt{2}}{1}}\) So, correct option is (4).
JEE - 2024
PHXI13:KINETIC THEORY
360240
The r.m.s velocity of a gas at a certain temperature is \(\sqrt{2}\) times than that of the oxygen molecules at that temperature. The gas can be:
1 \({H_2}\)
2 \(He\)
3 \(C{H_4}\)
4 \(S{O_2}\)
Explanation:
\(\quad v_{r m s} \propto \dfrac{1}{\sqrt{M}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{M_{2}}{M_{1}}}\) \(\Rightarrow \dfrac{v}{\sqrt{2} v}=\sqrt{\dfrac{M_{2}}{32}} \Rightarrow M_{2}=16\) So the given gas is \(C{H_4}\)
PHXI13:KINETIC THEORY
360241
At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at \(200 K\) ?
1 \(527^\circ C\)
2 \(1327^\circ C\)
3 \(2127^\circ C\)
4 \(2927^\circ C\)
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3 K T}{M}} \Rightarrow T \propto M\) \(\Rightarrow \dfrac{T_{1}}{T_{2}}=\dfrac{2}{32}\) \(\Rightarrow T_{2}=16 T_{1}=3200 \mathrm{~K}\) \( = 2927^\circ C\).
PHXI13:KINETIC THEORY
360242
Assertion : The rms velocity of gas molecules is doubled, when temperature of gas becomes four times. Reason : \(c \propto \sqrt{T}\).
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.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rms velocity of gas molecules is given by \(v_{\text {rms }}=c=\sqrt{\dfrac{3 k T}{m}}\) Hence, it is clear that when temperature becomes four times rms velocity will be two times.
360238
A mixture of two gases is contained in a vessel. The gas-I is monoatomic and gas-II is diatomic. The ratio of their molecular weights is \(1: 4\). The ratio of R.M.S. speeds of molecules of two gases will be
360239
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is
1 \({\dfrac{1}{32}}\)
2 \({\dfrac{1}{2 \sqrt{2}}}\)
3 \({\dfrac{1}{4}}\)
4 \({\dfrac{2 \sqrt{2}}{1}}\)
Explanation:
We know that, \({M_{O_{2}}=32, M_{H e}=4}\) \({R M S}\) velocity of a gas is given by \({v_{r m s}=\sqrt{\dfrac{3 R T}{M}} \Rightarrow v_{r m s} \propto \dfrac{1}{\sqrt{m}}}\) \({\Rightarrow \dfrac{v_{{He}}}{v_{O_{2}}}=\sqrt{\dfrac{M_{O_{2}}}{M_{{He}}}}=\sqrt{\dfrac{32}{4}}=\dfrac{2 \sqrt{2}}{1}}\) So, correct option is (4).
JEE - 2024
PHXI13:KINETIC THEORY
360240
The r.m.s velocity of a gas at a certain temperature is \(\sqrt{2}\) times than that of the oxygen molecules at that temperature. The gas can be:
1 \({H_2}\)
2 \(He\)
3 \(C{H_4}\)
4 \(S{O_2}\)
Explanation:
\(\quad v_{r m s} \propto \dfrac{1}{\sqrt{M}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{M_{2}}{M_{1}}}\) \(\Rightarrow \dfrac{v}{\sqrt{2} v}=\sqrt{\dfrac{M_{2}}{32}} \Rightarrow M_{2}=16\) So the given gas is \(C{H_4}\)
PHXI13:KINETIC THEORY
360241
At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at \(200 K\) ?
1 \(527^\circ C\)
2 \(1327^\circ C\)
3 \(2127^\circ C\)
4 \(2927^\circ C\)
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3 K T}{M}} \Rightarrow T \propto M\) \(\Rightarrow \dfrac{T_{1}}{T_{2}}=\dfrac{2}{32}\) \(\Rightarrow T_{2}=16 T_{1}=3200 \mathrm{~K}\) \( = 2927^\circ C\).
PHXI13:KINETIC THEORY
360242
Assertion : The rms velocity of gas molecules is doubled, when temperature of gas becomes four times. Reason : \(c \propto \sqrt{T}\).
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.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rms velocity of gas molecules is given by \(v_{\text {rms }}=c=\sqrt{\dfrac{3 k T}{m}}\) Hence, it is clear that when temperature becomes four times rms velocity will be two times.
360238
A mixture of two gases is contained in a vessel. The gas-I is monoatomic and gas-II is diatomic. The ratio of their molecular weights is \(1: 4\). The ratio of R.M.S. speeds of molecules of two gases will be
360239
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is
1 \({\dfrac{1}{32}}\)
2 \({\dfrac{1}{2 \sqrt{2}}}\)
3 \({\dfrac{1}{4}}\)
4 \({\dfrac{2 \sqrt{2}}{1}}\)
Explanation:
We know that, \({M_{O_{2}}=32, M_{H e}=4}\) \({R M S}\) velocity of a gas is given by \({v_{r m s}=\sqrt{\dfrac{3 R T}{M}} \Rightarrow v_{r m s} \propto \dfrac{1}{\sqrt{m}}}\) \({\Rightarrow \dfrac{v_{{He}}}{v_{O_{2}}}=\sqrt{\dfrac{M_{O_{2}}}{M_{{He}}}}=\sqrt{\dfrac{32}{4}}=\dfrac{2 \sqrt{2}}{1}}\) So, correct option is (4).
JEE - 2024
PHXI13:KINETIC THEORY
360240
The r.m.s velocity of a gas at a certain temperature is \(\sqrt{2}\) times than that of the oxygen molecules at that temperature. The gas can be:
1 \({H_2}\)
2 \(He\)
3 \(C{H_4}\)
4 \(S{O_2}\)
Explanation:
\(\quad v_{r m s} \propto \dfrac{1}{\sqrt{M}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{M_{2}}{M_{1}}}\) \(\Rightarrow \dfrac{v}{\sqrt{2} v}=\sqrt{\dfrac{M_{2}}{32}} \Rightarrow M_{2}=16\) So the given gas is \(C{H_4}\)
PHXI13:KINETIC THEORY
360241
At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at \(200 K\) ?
1 \(527^\circ C\)
2 \(1327^\circ C\)
3 \(2127^\circ C\)
4 \(2927^\circ C\)
Explanation:
\(V_{r m s}=\sqrt{\dfrac{3 K T}{M}} \Rightarrow T \propto M\) \(\Rightarrow \dfrac{T_{1}}{T_{2}}=\dfrac{2}{32}\) \(\Rightarrow T_{2}=16 T_{1}=3200 \mathrm{~K}\) \( = 2927^\circ C\).
PHXI13:KINETIC THEORY
360242
Assertion : The rms velocity of gas molecules is doubled, when temperature of gas becomes four times. Reason : \(c \propto \sqrt{T}\).
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.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rms velocity of gas molecules is given by \(v_{\text {rms }}=c=\sqrt{\dfrac{3 k T}{m}}\) Hence, it is clear that when temperature becomes four times rms velocity will be two times.
