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Q. No.Given below are two statements:
| Statement I: | If an ideal gas expands without any heat being supplied to it, then its temperature does not change. |
| Statement II: | If an ideal gas expands freely without any heat being supplied to it, then its internal energy remains unchanged. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Types of Processes |
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The same amount of heat is supplied to equimolar masses of hydrogen and helium, under constant pressure. The work done by the two gases, \(H_2\) and \(He,\) are \(W_1\) and \(W_2.\) Then:
| 1. | \(W_1>W_2\) |
| 2. | \(W_1<W_2\) |
| 3. | \(W_1=W_2\) |
| 4. | \(W_1\) and \(W_2\) cannot be compared unless the temperatures are known. |
Subtopic: Work Done by a Gas |
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A monoatomic ideal gas undergoes a process given by the equation: \({\dfrac{pT}{V}}=\text{constant.}\) The molar specific heat capacity in the process equals:
1. \({\dfrac{3}{2}}R\)
2. \({\dfrac{5}{2}}R\)
3. \({\dfrac{1}{2}}R\)
4. zero
1. \({\dfrac{3}{2}}R\)
2. \({\dfrac{5}{2}}R\)
3. \({\dfrac{1}{2}}R\)
4. zero
Subtopic: Molar Specific Heat |
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The quantity of heat required to take a system from \(\mathrm{A}\) to \(\mathrm{C}\) through the process \(\mathrm{ABC}\) is \(20\) cal. The quantity of heat required to go from \(\mathrm{A}\) to \(\mathrm{C}\) directly is:
1. \(20\) cal
2. \(24.2\) cal
3. \(21\) cal
4. \(23\) cal
Subtopic: Cyclic Process |
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An ideal monoatomic gas at a temperature of \(300\) K and a pressure of \(10\) atm is suddenly allowed to expand into vacuum so that its volume is doubled. No exchange of heat is allowed to take place between the gas and its surroundings during the process. After equilibrium is reached, the final temperature is:
| 1. | \(300\) K | 2. | \(\dfrac{300}{2^{5/3}}\) K |
| 3. | \(\dfrac{300}{2^{2/3}}\) K | 4. | \(600\) K |
Subtopic: Types of Processes |
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Two monoatomic gases \(A,B\) are taken in two parts of a vessel having equal volumes \(V_0.\) The gases are at the same pressure \(P_0\) but at temperature of \(300~\text K\) and \(600~\text K.\) There is a partition between the parts of the vessel. The partition is removed, and the gases are allowed to mix. The vessel, as a whole, is insulated. The final temperature of the system is:
1. \(450~\text K\)
2. \(400~\text K\)
3. \(500~\text K\)
4. \(550~\text K\)
1. \(450~\text K\)
2. \(400~\text K\)
3. \(500~\text K\)
4. \(550~\text K\)
Subtopic: Work Done by a Gas |
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An ideal gas forms the working substance of a Carnot engine, and is taken around the Carnot cycle. We form the integral: \(I=\int\dfrac{dQ}{T},\)
where \(dQ\) is the heat supplied to the gas and \(T\) is the temperature of the gas. The integral is evaluated over the entire cycle. The value of the integral \(I\) is:
where \(dQ\) is the heat supplied to the gas and \(T\) is the temperature of the gas. The integral is evaluated over the entire cycle. The value of the integral \(I\) is:
| 1. | zero |
| 2. | negative |
| 3. | positive |
| 4. | non-negative(positive or zero) |
Subtopic: Carnot Engine |
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A gas \((\gamma = 1.5)\) undergoes a process in which its volume is doubled, but the speed of sound in the gas remains unchanged. Then,
| 1. | the pressure is halved |
| 2. | the pressure decreases by a factor of \(2\sqrt 2\) |
| 3. | the temperature is halved |
| 4. | the temperature decreases by a factor of \(2 \sqrt 2\) |
Subtopic: Types of Processes |
50%
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Given below are two statements:
| Statement I: | The efficiency of any thermodynamic engine can approach \(100\%\) if friction and all dissipative processes are reduced. |
| Statement II: | The first law of thermodynamics is applicable only to non-living systems. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Second Law of Thermodynamics |
54%
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An ideal mono-atomic gas undergoes an expansion, keeping its temperature constant, but its volume increases two-fold. The same amount (number of moles) of a diatomic gas undergoes the same process. If the heat supplied in the first case be \(Q_1\) and in the second be \(Q_2,\) then:
| 1. | \(Q_1=Q_2\) | 2. | \(5Q_1=3Q_2\) |
| 3. | \(Q_1=2Q_2\) | 4. | \(Q_2=2Q_1\) |
Subtopic: Types of Processes |
58%
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