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Q. No.Given below are two statements:
Choose the correct answer from the options given below.
| Assertion (A): | If the average kinetic energy of \(H_2\) and \(O_2\) molecules, kept in two different sized containers are same, then their temperatures will be same. |
| Reason (R): | Then r.m.s. speed of \(H_2\) and \(O_2\) molecules are same at same temperature. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Types of Velocities |
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A mixture of carbon dioxide and oxygen has volume \(8310~\text{cm}^{3},\) temperature \(300~\text{K},\) pressure \(100~\text{kPa}\) and mass \(13.2~\text{g}.\) The number of moles of carbon dioxide and oxygen gases in the mixture respectively are:
(Assume both carbon dioxide and oxygen gases behave like ideal gases)\([{R}=8.31~ \text{J/mol K} ]\)
1. \(0.15~\text{and}~0.18 \)
2. \(0.25~\text{and}~0.08 \)
3. \(0.21~\text{and}~0.12 \)
4. \(0.13~\text{and}~0.20 \)
(Assume both carbon dioxide and oxygen gases behave like ideal gases)\([{R}=8.31~ \text{J/mol K} ]\)
1. \(0.15~\text{and}~0.18 \)
2. \(0.25~\text{and}~0.08 \)
3. \(0.21~\text{and}~0.12 \)
4. \(0.13~\text{and}~0.20 \)
Subtopic: Ideal Gas Equation |
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Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure \(90~\text{kPa}\) and temperature \(400~\text{K}.\) Keeping the temperature of one vessel constant at \(400~\text{K}\) the second vessel temperature is raised to \(500~\text{K}.\) The final pressure in the vessels is: (in kPa)
1. \(100\)
2. \(120\)
3. \(90\)
4. \(105\)
1. \(100\)
2. \(120\)
3. \(90\)
4. \(105\)
Subtopic: Ideal Gas Equation |
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Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \(\Delta {Q}: \Delta {U}: \Delta {W}\) is:
1. \(2: 3: 5\)
2. \(5: 3: 2\)
3. \(2: 5: 7\)
4. \(7: 5: 2\)
1. \(2: 3: 5\)
2. \(5: 3: 2\)
3. \(2: 5: 7\)
4. \(7: 5: 2\)
Subtopic: Specific Heat |
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One gas of \(n_1\) mole of molecules at temperature \(T_1\), volume \(V_1\), and pressure \(P_1\), and another gas of \(n_2\) mole of molecules at temperature \(T_2\), volume \(V_2\) and pressure \(P_2\), are mixed resulting in pressure \(P\) and volume \(V\) of the mixture. The temperature of the mixture is:
1. \(\dfrac{\left({T}_1+{T}_2\right)}{2}\)
2. \(\dfrac{{T}_1 {~T}_2 {PV}}{ \left({T}_2 {P}_1 {~V}_1+{T}_1 {P}_2 {~V}_2\right)}\)
3. \(\dfrac{\left(T_2 P_1 V_1+T_1 P_2 V_2\right)}{ \left(T_1 T_2 P V\right)}\)
4. \(\dfrac{\left|T_1-T_2\right|}{2}\)
1. \(\dfrac{\left({T}_1+{T}_2\right)}{2}\)
2. \(\dfrac{{T}_1 {~T}_2 {PV}}{ \left({T}_2 {P}_1 {~V}_1+{T}_1 {P}_2 {~V}_2\right)}\)
3. \(\dfrac{\left(T_2 P_1 V_1+T_1 P_2 V_2\right)}{ \left(T_1 T_2 P V\right)}\)
4. \(\dfrac{\left|T_1-T_2\right|}{2}\)
Subtopic: Ideal Gas Equation |
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An ideal gas undergoes a process maintaining relation between pressure (\(P\)) and volume (\(V\)) as \(P=P_{{0}}\left(1+\left(\dfrac{V_{{0}}}{V}\right)^2\right)^{-1}\), where \(P_0\) and \(V_0\) are constants. If two simples \(A\) and \(B\) (two moles each) with initial volumes \(V_0\) and \(3V_0\) respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, \(T_B-T_A\) is:
(\(R=\) gas constant)
1. \(\dfrac{9 P_{{0}} V_{{0}}}{8 R}\)
2. \(\dfrac{11 P_{{0}} V_{{0}}}{10 R}\)
3. \(\dfrac{7 P_{{0}} V_{{0}}}{6 R}\)
4. \(\dfrac{13 P_{{0}} V_{{0}}}{11 R}\)
(\(R=\) gas constant)
1. \(\dfrac{9 P_{{0}} V_{{0}}}{8 R}\)
2. \(\dfrac{11 P_{{0}} V_{{0}}}{10 R}\)
3. \(\dfrac{7 P_{{0}} V_{{0}}}{6 R}\)
4. \(\dfrac{13 P_{{0}} V_{{0}}}{11 R}\)
Subtopic: Ideal Gas Equation |
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The root mean square (rms) speed of oxygen molecules at \(47^\circ \text{C}\) is equal to that of hydrogen molecules at what temperature (in \(^\circ \text{C}\))?
1. \(-235\)
2. \(-100\)
3. \(-253\)
4. \(-20\)
1. \(-235\)
2. \(-100\)
3. \(-253\)
4. \(-20\)
Subtopic: Types of Velocities |
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Consider two boxes containing ideal gases \(A\) and \(B\) such that their temperatures, pressures and number densities are same. The molecular size of \(A\) is half of that of \(B\) and mass of molecule \(A\) is four times that of \(B\). If the collision frequency in gas \(B\) is \(32\times10^{18}~\text{/s}\) then collision frequency in gas \(A\) is:
1. \(32\times10^{8}\) /s
2. \(4\times10^{8}\) /s
3. \(2\times10^{8}\) /s
4. \(8\times10^{8}\) /s
1. \(32\times10^{8}\) /s
2. \(4\times10^{8}\) /s
3. \(2\times10^{8}\) /s
4. \(8\times10^{8}\) /s
Subtopic: Mean Free Path |
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An insulated cylinder of volume \(60 ~\text{cm}^3\) is filled with a gas at \(27~^\circ\text{C}\) and \(2\) atmospheric pressure. Then the gas is compressed making the final volume as \(20 ~\text{cm}^3\) while allowing the temperature to rise to \(77~^\circ\text{C}.\) The final pressure is: (in atmospheric pressure)
1. \(3\)
2. \(5\)
3. \(7\)
4. \(9\)
1. \(3\)
2. \(5\)
3. \(7\)
4. \(9\)
Subtopic: Ideal Gas Equation |
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An air bubble of volume \(2.9\) cm3 rises from the bottom of a swimming pool of \(5\) m deep. At the bottom of the pool water temperature is \(17^{\circ}\text{C}\). The volume of the bubble when it reaches the surface, where the water temperature is \(27^{\circ}\text{C}\), is: (in cm3) (\(g= 10~\text{m/s}^2\), density of water = \(10^{3}\) kg/m3, and \(1\) atm pressure is \(10^{5}\) Pa)
1. \(4.2\)
2. \(2.0\)
3. \(3.0\)
4. \(4.5\)
1. \(4.2\)
2. \(2.0\)
3. \(3.0\)
4. \(4.5\)
Subtopic: Ideal Gas Equation |
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