Q. No.A Carnot engine \(E\) is working between two temperatures \(473~\text{K}\) and \(273~\text{K}.\) In a new system, two engines \(E_1\) works between \(473~\text{K}\) to \(373~\text{K}\) and engine \(E_2\) works between \(373~\text{K}\) to \(273~\text{K}.\) If \(\eta_{12}, ~\eta_1\) and \(\eta_2\) are the efficiencies of the engines, \(E,\) \(E_1\) and, \(E_2\) respectively, then:
1. \(\eta_{12}=\eta_1 \eta_2\)
2. \(\eta_{12}<\eta_1+\eta_2\)
3. \(\eta_{12} \geq \eta_1+\eta_2\)
4. \(\eta_{12}=\eta_1+\eta_2\)
1. \(\eta_{12}=\eta_1 \eta_2\)
2. \(\eta_{12}<\eta_1+\eta_2\)
3. \(\eta_{12} \geq \eta_1+\eta_2\)
4. \(\eta_{12}=\eta_1+\eta_2\)
Subtopic: Β Carnot Engine |
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A Carnot engine operates between temperatures of \(27^\circ \mathrm C\) and \(127^\circ \mathrm C\) and performs \(2\) kJ of work. The amount of heat energy rejected is:
| 1. | \(4\) kJ | 2. | \(6\) kJ |
| 3. | \(8\) kJ | 4. | \(12\) kJ |
Subtopic: Β Carnot Engine |
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A Carnot engine working between a source and a sink at \(200~\text K\) has an efficiency of \(50\%.\) Another Carnot engine working between the same source and another sink with an unknown temperature \(T\) has an efficiency of \(75\text{%}.\) The value of \(T\) is equal to:
1. \(400 ~\text K\)
2. \(300 ~\text K\)
3. \(200 ~\text K\)
4. \(100 ~\text K\)
1. \(400 ~\text K\)
2. \(300 ~\text K\)
3. \(200 ~\text K\)
4. \(100 ~\text K\)
Subtopic: Β Carnot Engine |
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If Carnot engines work between the freezing point and boiling point of water, then the efficiency of a Carnot engine is:
1. \(35\)%
2. \(27\)%
3. \(22\)%
4. \(17\)%
1. \(35\)%
2. \(27\)%
3. \(22\)%
4. \(17\)%
Subtopic: Β Carnot Engine |
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):
In the light of the above statements choose the correct answer from the options given below:
| Assertion (A): | At a sink temperature of \(-273^{\circ}\) C, the efficiency of a Carnot engine will be 1. |
| Reason (R): | The efficiency of a Carnot engine is given by \(\eta=1-{{T_{\sin k}}\over{T_{source}}}\) |
In the light of the above statements choose the correct answer from the options given below:
| 1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
| 3. | (A) is true but (R) is false. |
| 4. | (A) is false but (R) is true. |
Subtopic: Β Carnot Engine |
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For a heat engine based on the Carnot cycle source is at a temperature \(600~\mathrm{K}\). Now if source temperature is doubled then efficiency also gets doubled while keeping the sink temperature same at \(x ~\mathrm{K}\). The value of \(x \) is equal to:
1. \(400\)
2. \(600\)
3. \(200\)
4. \(300\)
1. \(400\)
2. \(600\)
3. \(200\)
4. \(300\)
Subtopic: Β Carnot Engine |
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In a Carnot engine, the temperature of the reservoir is \(527^\circ \text{C}\) and that of the sink is \(200\) K. If the work done by the engine when it transfers heat from the reservoir to sink is \(12000\) kJ, the quantity of heat absorbed by the engine from the reservoir is:
1. \(12\times10^6\) J
2. \(14\times10^6\) J
3. \(16\times10^6\) J
4. \(18\times10^6\) J
1. \(12\times10^6\) J
2. \(14\times10^6\) J
3. \(16\times10^6\) J
4. \(18\times10^6\) J
Subtopic: Β Carnot Engine |
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The efficiency of a Carnot's engine, working between the steam point and ice point, will be:
| 1. | \(26.81\text{%}\) | 2. | \(37.81\text{%}\) |
| 3. | \(47.81\text{%}\) | 4. | \(57.81\text{%}\) |
Subtopic: Β Carnot Engine |
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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: Β Carnot Engine |
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A Carnot engine whose heat sinks at \(27^\circ \text{C},\) has an efficiency of \(25\text{%}.\) By how many degrees should the temperature of the source be changed to increase the efficiency by \(100\text{%}\) of the original efficiency?
1. Increase by \(18^\circ \text{C}\)
2. Increase by \(200^\circ \text{C}\)
3. Increase by \(120^\circ \text{C}\)
4. Increase by \(73^\circ \text{C}\)
1. Increase by \(18^\circ \text{C}\)
2. Increase by \(200^\circ \text{C}\)
3. Increase by \(120^\circ \text{C}\)
4. Increase by \(73^\circ \text{C}\)
Subtopic: Β Carnot Engine |
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