Q. No.The efficiency of an ideal heat engine is less than \(100\%\) because of:
| 1. | the presence of friction. |
| 2. | the leakage of heat energy. |
| 3. | unavailability of the sink at zero kelvin. |
| 4. | all of these. |
An ideal gas heat engine operates in a Carnot cycle between 227ºC and 127ºC. It absorbs 6 × 104 cals of heat at higher temperatures.
The amount of heat converted to work will be?
1. 4.8 × 104 cals
2. 2.4 × 104 cals
3. 1.2 × 104 cals
4. 6 × 104 cals
In a Carnot engine, when \(T_2=0^\circ \mathrm{C}\) and \(T_1=200^\circ \mathrm{C},\) its efficiency is \(\eta_1\) and when \(T_1=0^\circ \mathrm{C}\) and \(T_2=-200^\circ \mathrm{C},\) its efficiency is \(\eta_2.\) What is the value of \(\frac{\eta_1}{\eta_2}?\)
| 1. | 0.577 | 2. | 0.733 |
| 3. | 0.638 | 4. | cannot be calculated |
1. \(\frac{\eta}{2}\)
2. \(\eta\)
3. \(2\eta\)
4. \(3\eta\)
Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at \(T_1=800\) K and rejects to sink at \(T_2\) K. The second engine, B, receives heat rejected by the first engine and rejects to another sink at \(T_3=300\) K. If the work outputs of the two engines are equal, then the value of \(T_2\) will be:
| 1. | 100 K | 2. | 300 K |
| 3. | 550 K | 4. | 700 K |
A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by \(62^{\circ}\mathrm{C}\), the efficiency of the engine is doubled. The temperatures of the source and sink are:
1. \(80^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)
2. \(95^{\circ}\mathrm{C}, 28^{\circ}\mathrm{C}\)
3. \(90^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)
4. \(99^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)
If the temperature of the source and the sink in the heat engine is at 1000 K & 500 K respectively, then the efficiency can be:
1. 20%
2. 30%
3. 50%
4. All of these
Two Carnot engines x and y are working between the same source temperature \(T_1\) and the same sink temperature \(T_2\). If the temperature of the source in Carnot engine x is increased by \(\Delta T\), and in the Carnot engine y, the temperature of the sink is increased by\(\Delta T\), then the efficiency of x and y becomes \(\eta_\mathrm x\) and\(\eta_\mathrm y\). Then:
| 1. | \(\eta_{\mathrm{x}}=\eta_{\mathrm{y}}\) |
| 2. | \(\eta_{\mathrm{x}}<\eta_{\mathrm{y}}\) |
| 3. | \(\eta_{\mathrm{x}}>\eta_{\mathrm{y}}\) |
| 4. | The relation between \(\eta_{\mathrm{x}}\) and \(\eta_{\mathrm{y}}\) depends on the nature of the working substance |
A heat engine operates between the temperatures of 300 K and 500 K. If it extracts 1200 J of heat energy from the source, then the maximum amount of work that can be done by the engine is:
1. 720 J
2. 520 J
3. 480 J
4. 200 J
The efficiency of a Carnot heat engine working between the temperatures \(27^{\circ}\mathrm{C}\) and \(227^{\circ}\mathrm{C}\) is:
1. 0.1
2. 0.6
3. 0.2
4. 0.4
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