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Q. No.The pressure of an ideal gas \(\left(\gamma=\dfrac32\right)\) is increased by \(1\%\) in an adiabatic process. The temperature of the gas:
1.
increases by \(1.5\%\)
2.
decreases by \(1.5\%\)
3.
increases by \(\frac13\%\)
4.
increases by \(\frac23\%\)
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 |
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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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A gas undergoes an isothermal process. The specific heat capacity of the gas in the process is:
| 1. | infinity | 2. | \(0.5\) |
| 3. | zero | 4. | \(1\) |
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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A thermodynamic process involving a system takes place with \(100~\text{J}\) of heat being rejected to the environment and an increase of \(20~\text{J}\) of internal energy. Then,
| 1. | work done by the system is \(120~\text{J}.\) |
| 2. | work done on the system is \(120~\text{J}.\) |
| 3. | work done by the system is \(80~\text{J}.\) |
| 4. | work done on the system is \(80~\text{J}.\) |
Subtopic: First Law of Thermodynamics |
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The internal energy of a gas is given by \(U=\dfrac32PV.\) The gas expands in such a way that its internal energy (initially \(U_0\)) remains constant throughout the process, but its volume changes from \(V_0\) to \(2V_0.\) The heat supplied to the gas equals:
| 1. | \(U_0\mathrm{ln}(2)\) | 2. | \(\dfrac12U_0~\mathrm{ln}(2)\) |
| 3. | \(\dfrac13U_0~\mathrm{ln}(2)\) | 4. | \(\dfrac23U_0~\mathrm{ln}(2)\) |
Subtopic: First Law of Thermodynamics |
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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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Which of the following relations does not give the equation of an adiabatic process, where terms have their usual meaning?
1. \({P}^{1-\gamma}{T}^{\gamma}= \text{constant}\)
2. \({PV}^{\gamma}=\text{constant}\)
3. \({TV}^{\gamma-1}= \text{constant}\)
4. \({P}^{\gamma} {T}^{1-\gamma}=\text{constant}\)
1. \({P}^{1-\gamma}{T}^{\gamma}= \text{constant}\)
2. \({PV}^{\gamma}=\text{constant}\)
3. \({TV}^{\gamma-1}= \text{constant}\)
4. \({P}^{\gamma} {T}^{1-\gamma}=\text{constant}\)
Subtopic: Types of Processes |
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NEET - 2013
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The ratio \(C_P/C_V=1.5\) for a certain ideal gas. The gas is taken at an initial pressure of \(2\) kPa and compressed suddenly to \(\dfrac14\) of its initial volume. The final pressure is:
1. \(\dfrac12\) kPa
2. \(4\) kPa
3. \(8\) kPa
4. \(16\) kPa
Subtopic: Types of Processes |
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