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Q. No.For an ideal gas at temperature \(T,\) the average force exerted by a single molecule on the walls of a closed container depends on \({T}\) as \(T^q.\) Which of the following is a good estimate for \(q\)?
1.
\(\dfrac{1}{4}\)
2.
\(2\)
3.
\(\dfrac{1}{3}\)
4.
\(1\)
Subtopic: Kinetic Energy of an Ideal Gas |
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Using equipartition of energy, the specific heat (in \(\text{J kg}^{-1}\text{K}^{-1}\) ) of aluminum at room temperature can be estimated to be:
(atomic weight of aluminum=27)
1. \(410\)
2. \(25\)
3. \(1850\)
4. \(925\)
(atomic weight of aluminum=27)
1. \(410\)
2. \(25\)
3. \(1850\)
4. \(925\)
Subtopic: Law of Equipartition of Energy |
Level 3: 35%-60%
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An ideal gas has molecules with \(5\) degrees of freedom. The ratio of specific heats at constant pressure \(C_{P}\) and at constant volume \(C_V\) is:
1. \(\frac{7}{2}\)
2. \(\frac{7}{5}\)
3. \(6\)
4. \(\frac{5}{2}\)
1. \(\frac{7}{2}\)
2. \(\frac{7}{5}\)
3. \(6\)
4. \(\frac{5}{2}\)
Subtopic: Specific Heat |
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Two moles of helium are mixed with \(n\) moles of hydrogen. If \(\frac{c_p}{c_v}=\frac{3}{2}\) for the mixture then, the value of \(n\) is:
1. \(1\)
2. \(3\)
3. \(2\)
4. \(\dfrac{3}{2}\)
1. \(1\)
2. \(3\)
3. \(2\)
4. \(\dfrac{3}{2}\)
Subtopic: Law of Equipartition of Energy |
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Find the total kinetic energy of \(1\) mole of oxygen gas at \(27^{\circ} \text{C}. \left[\text {Take } R=\frac{25}{3} \text{J} / \text{mol}\text{-K}\right]\)
1. \(6250~\text{J}\)
2. \(3125~\text{J}\)
3. \(12500~\text{J}\)
4. \(625~\text{J}\)
1. \(6250~\text{J}\)
2. \(3125~\text{J}\)
3. \(12500~\text{J}\)
4. \(625~\text{J}\)
Subtopic: Kinetic Energy of an Ideal Gas |
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Level 2: 60%+
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\(N\) moles of non-linear polyatomic gas (degree of freedom \(6\)) is mixed with \(2\) moles of monoatomic gas. The resultant mixture has molar-specific heat equal to that of a diatomic gas, then the number of moles \((N)\) is:
1. \(4\)
2. \(5\)
3. \(6\)
4. \(3\)
1. \(4\)
2. \(5\)
3. \(6\)
4. \(3\)
Subtopic: Specific Heat |
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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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Level 1: 80%+
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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. \(1 / 32\)
2. \(1 /(2 \sqrt2)\)
3. \(1 / 4\)
4. \((2 \sqrt 2) / 1\)
1. \(1 / 32\)
2. \(1 /(2 \sqrt2)\)
3. \(1 / 4\)
4. \((2 \sqrt 2) / 1\)
Subtopic: Types of Velocities |
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Energy of \(10\) non rigid diatomic molecules at temperature T is :
1. \(35\) KBT
2. \(35\) RT
3. \(\frac{7}{2}\) RT
4. \(70\) KBT
Subtopic: Law of Equipartition of Energy |
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The temperature of a gas is \(-78^{\circ} \) and the average translational kinetic energy of its molecules is \(K.\) The temperature at which the average translational kinetic energy of the molecules of the same gas becomes \(2K\) is
| 1. | \(-39^{\circ} \mathrm{C}\) | 2. | \(127^{\circ} \mathrm{C}\) |
| 3. | \(-78^{\circ} \mathrm{C}\) | 4. | \(117^{\circ} \mathrm{C}\) |
Subtopic: Kinetic Energy of an Ideal Gas |
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