Q. No.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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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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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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A gas of certain mass filled in a closed cylinder at a pressure of \(3.23~\text{kPa}\) has temperature \(50^\circ \text{C}.\) The gas is now heated to double its temperature. The modified pressure is: (in Pa)
1. \(3200\)
2. \(3730\)
3. \(3600\)
4. \(3450\)
1. \(3200\)
2. \(3730\)
3. \(3600\)
4. \(3450\)
Subtopic: Ideal Gas Equation |
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There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at \(8 ~\text{kPa} \) at \(1000 ~\text K\) while the smaller vessel contains the gas at \(7 ~\text{kPa}\) at \(500 ~\text K.\) If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at \(600 ~\text K,\) at steady state the pressure in the vessels will be (in \(\text{kPa}\)):
1. \(6\)
2. \(24\)
3. \(18\)
4. \(4.4\)
1. \(6\)
2. \(24\)
3. \(18\)
4. \(4.4\)
Subtopic: Ideal Gas Equation |
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In a container, \(1~\text{g}\) of hydrogen and \(1~\text{g}\) of oxygen are taken. Find the ratio of hydrogen pressure to oxygen pressure.
1. \(16\)
2. \(12\)
3. \(18\)
4. \(20\)
1. \(16\)
2. \(12\)
3. \(18\)
4. \(20\)
Subtopic: Ideal Gas Equation |
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A given gas is taken through three different processes at three different densities \(\rho_1, \rho_2 \) and \(\rho_3.\) The corresponding \(P\text-T\) graphs are given. Then:
1. \(\rho_3>\rho_2>\rho_1 \)
2. \(\rho_3<\rho_2>\rho_1 \)
3. \(\rho_3<\rho_2<\rho_1\)
4. \(\rho_3>\rho_2<\rho_1\)
1. \(\rho_3>\rho_2>\rho_1 \)
2. \(\rho_3<\rho_2>\rho_1 \)
3. \(\rho_3<\rho_2<\rho_1\)
4. \(\rho_3>\rho_2<\rho_1\)
Subtopic: Ideal Gas Equation |
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