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Q. No.A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by \(62^\circ \text{C}\), the efficiency of the engine is doubled. The temperatures of the source and the sink are:
1. \(90^\circ \text{C}\), \(37^\circ \text{C}\)
2. \(99^\circ \text{C}\), \(37^\circ \text{C}\)
3. \(80^\circ \text{C}\), \(37^\circ \text{C}\)
4. \(95^\circ \text{C}\), \(37^\circ \text{C}\)
Subtopic: Carnot Engine |
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A cylinder of a fixed capacity of \(44.8\) litres contains helium gas at a standard temperature and pressure. The amount of heat needed to raise the temperature of the gas in the cylinder by \(20.0^\circ \text{C}\) will be: (Given: gas constant R = \(8.3\) JK–1-moI–1)
1. \(249\) J
2. \(415\) J
3. \(498\) J
4. \(830\) J
1. \(249\) J
2. \(415\) J
3. \(498\) J
4. \(830\) J
Subtopic: Types of Processes |
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Level 2: 60%+
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Starting with the same initial conditions, an ideal gas expands from volume \(V_1\) to \(V_2\) in three different ways. The work done by the gas is \(W_1\) if the process is purely isothermal, \(W_2\) if the process is purely adiabatic and \(W_3\) if the process is purely isobaric. Then,
| 1. | \(W_1<W_2<W_3\) | 2. | \(W_2<W_3<W_1\) |
| 3. | \(W_3<W_1<W_2\) | 4. | \(W_2<W_1<W_3\) |
Subtopic: Types of Processes |
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A fixed mass of an ideal gas undergoes a change in which it is supplied with \(3500\) J of thermal energy. At the same time, this gas does \(3500\) J of work on its surroundings. Which type of change does the gas undergo during this time?
| 1. | adiabatic | 2. | isothermal |
| 3. | isochoric | 4. | isomeric |
Subtopic: First Law of Thermodynamics |
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If an ideal gas is compressed isothermally, which of the following statement is true?
| 1. | Energy is transferred into the gas by heat. |
| 2. | Work is done by the gas. |
| 3. | Pressure of the gas decreases. |
| 4. | The internal energy of the gas remains constant. |
Subtopic: Types of Processes |
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Level 1: 80%+
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In a certain process, \(33.5\) kJ is furnished to the system while the system does \(6\) kJ of work. What is the change in the internal energy of the system?
1. \(39.5\) kJ
2. \(33.5\) kJ
3. \(27.5\) kJ
4. \(6\) kJ
1. \(39.5\) kJ
2. \(33.5\) kJ
3. \(27.5\) kJ
4. \(6\) kJ
Subtopic: First Law of Thermodynamics |
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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 heat engine (Carnot engine) operates between a cold reservoir at temperature \(T_2=300\) K and a hot reservoir at temperature \(T_1.\) If it were to take \(100\) J of heat from the hot reservoir and deliver \(80\) J of heat to the cold reservoir in each cycle, the minimum temperature of the hot reservoir would be:
1. \(350\) K
2. \(375\) K
3. \(400\) K
4. \(450\) K
1. \(350\) K
2. \(375\) K
3. \(400\) K
4. \(450\) K
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 |
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Level 2: 60%+
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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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Level 3: 35%-60%
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