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Q. No.In \(1^{\text{st}}\) case, Carnot engine operates between temperatures \(300\) K and \(100\) K. In \(2^{\text{nd}}\) case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in \(2^{\text{nd}}\) case) will be:
1.
same as the \(1^{\text{st}}\) case.
2.
always greater than the \(1^{\text{st}}\) case.
3.
always less than the \(1^{\text{st}}\) case.
4.
may increase or decrease with respect to the \(1^{\text{st}}\) case.
Subtopic: Carnot Engine |
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A Carnot engine has an efficiency of \(50\%\). If the temperature of sink is reduced by \(40^{\circ}\text{C}\), its efficiency increases by \(30\%\). The temperature of the source will be:
1. \(166.7\) K
2. \(255.1\) K
3. \(266.7\) K
4. \(367.7\) K
1. \(166.7\) K
2. \(255.1\) K
3. \(266.7\) K
4. \(367.7\) K
Subtopic: Carnot Engine |
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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 |
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A Carnot engine takes \(5000~\text{kcal}\) of heat from a reservoir at \(727^\circ \text{C}\) and gives heat to a sink at \(127^\circ \text{C}.\) The work done by the engine is:
1. \(3 \times 10^6 ~\text J\)
2. zero
3. \(12.6 \times 10^6 \)
4. \(8.4 \times 10^6 \)
1. \(3 \times 10^6 ~\text J\)
2. zero
3. \(12.6 \times 10^6 \)
4. \(8.4 \times 10^6 \)
Subtopic: Carnot Engine |
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A monoatomic gas performs a work of \(\dfrac{ Q} {4}\) where \(Q\) is the heat supplied to it. During this transformation, the molar heat capacity of the gas will be: (\(R\) is the gas constant.)
| 1. | \(R\) | 2. | \(2R\) |
| 3. | \(3R\) | 4. | \(4R\) |
Subtopic: Molar Specific Heat |
59%
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A thermally insulated vessel contains an ideal gas of molecular mass \(M\) and a specific heat ratio of \(1.4.\) The vessel is moving with speed \(v\) and is suddenly brought to rest. Assuming no heat is lost to the surroundings, then the vessel temperature of the gas increases by:
(\(R=\) universal gas constant)
(\(R=\) universal gas constant)
| 1. | \(\dfrac{M v^2}{7 R} \) | 2. | \(\dfrac{M v^2}{5 R} \) |
| 3. | \(\dfrac{2M v^2}{7 R} \) | 4. | \(\dfrac{7M v^2}{5 R} \) |
Subtopic: Molar Specific Heat |
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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 |
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If \(\Delta Q\) is the heat flowing out of a system, \(\Delta W\) is the work done by the system on its surroundings, and \(\Delta U\) is the decrease in internal energy of the system, then the first law of thermodynamics can be stated as:
| 1. | \(\Delta Q=\Delta U+\Delta W\) |
| 2. | \(\Delta U=\Delta Q+\Delta W\) |
| 3. | \(\Delta U=\Delta Q-\Delta W\) |
| 4. | \(\Delta U+\Delta Q+\Delta W=0\) |
Subtopic: First Law of Thermodynamics |
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An ideal monatomic gas and a diatomic gas, both undergo adiabatic expansion starting from the same point on the \(P\)-\(V\) (indicator) diagram. The gases also undergo isothermal expansion. The curves are given by \(a,b,c.\) Which of the following is correct?
| 1. | \(a\)–isothermal, \(b\)–monatomic adiabatic, \(c\)–diatomic adiabatic |
| 2. | \(a\)–monatomic adiabatic, \(b\)–diatomic adiabatic, \(c\)–isothermal |
| 3. | \(a\)–diatomic adiabatic, \(b\)–monatomic adiabatic, \(c\)–isothermal |
| 4. | \(a\)–isothermal, \(b\)–diatomic adiabatic, \(c\)–monatomic adiabatic |
Subtopic: Types of Processes |
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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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