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Q. No.\(n\) moles of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.
\(A\rightarrow B\)
Isothermal expansion at temperature \(T\) so that the volume is doubled from \(V_1\) to \(V_2=2V_1\) and pressure changes from \(P_1\) to \(P_2.\)
\(B\rightarrow C\)
Isobaric compression at pressure \(P_2\) to initial volume \(V_1\).
\(C\rightarrow A\)
Isochoric change leading to change of pressure from \(P_2\) to \(P_1\).
Total work done in the complete cycle \(ABCA\) is:
1. \(0\)
2. \(nRT(\ln 2-\frac{1}{2})\)
3. \(nRT\ln 2\)
4. \(nRT(\ln 2+\frac{1}{2})\)
2. \(nRT(\ln 2-\frac{1}{2})\)
3. \(nRT\ln 2\)
4. \(nRT(\ln 2+\frac{1}{2})\)
Subtopic: Work Done by a Gas |
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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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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 |
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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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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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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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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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