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A monoatomic ideal gas, initially at temperature \(T_1\), is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature \(T_2\) by releasing the piston suddenly. If \(L_1\) and \(L_2\)_{ }are the lengths of the gas column before and after expansion, respectively, then \(\frac{T_1}{T_2}\) is given by:

1. \(\left(\frac{L_1}{L_2}\right)^{\frac{2}{3}}\)

2. \(\frac{L_1}{L_2}\)

3. \(\frac{L_2}{L_1}\)

4. \(\left(\frac{L_2}{L_1}\right)^{\frac{2}{3}}\)

Subtopic: Types of Processes |

70%

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An insulator container contains 4 moles of an ideal diatomic gas at a temperature T. If heat *Q* is supplied to this gas, due to which 2 moles of the gas are dissociated into atoms, but the temperature of the gas remains constant, then:

1. *Q* = 2*RT*

2. *Q* = *RT*

3. *Q* = 3*RT*

4. *Q* = 4*RT*

Subtopic: First Law of Thermodynamics |

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The volume of air (diatomic) increases by \(5\%\) in its adiabatical expansion. The percentage decrease in its pressure will be:

1. | \(5\%\) | 2. | \(6\%\) |

3. | \(7\%\) | 4. | \(8\%\) |

Subtopic: Types of Processes |

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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 |

Subtopic: Carnot Engine |

73%

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The initial pressure and volume of a gas are \(P\) and *\(V\),* respectively. First, it is expanded isothermally to volume \(4V\) and then compressed adiabatically to volume *\(V\)*. The final pressure of the gas will be: [Given: \(\gamma = 1.5\)]

1. | \(P\) | 2. | \(2P\) |

3. | \(4P\) | 4. | \(8P\) |

Subtopic: Types of Processes |

74%

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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. \(99^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)

Subtopic: Carnot Engine |

61%

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An ideal gas is taken from point *A* to point *B, *as shown in the *P-V* diagram. The work done in the process is:

** **

1. $({P}_{A}-{P}_{B})({V}_{B}-{V}_{A})$

2. $\frac{1}{2}({P}_{B}-{P}_{A})({V}_{B}+{V}_{A})$

3. $\frac{1}{2}({P}_{B}-{P}_{A})({V}_{B}-{V}_{A})$

4. $\frac{1}{2}({P}_{B}+{P}_{A})({V}_{B}-{V}_{A})$

Subtopic: Work Done by a Gas |

52%

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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

Subtopic: Carnot Engine |

54%

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In an adiabatic process, the graph for work done versus change of temperature \(\Delta T\) will be:

1. | 2. | ||

3. | 4. |

Subtopic: Work Done by a Gas |

63%

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If n moles of an ideal gas is heated at a constant pressure from 50°C to 100°C, the increase in the internal energy of the gas will be: \(\left(\frac{C_{p}}{C_{v}} = \gamma\ and\ R = gas\ constant\right)\)

1. | \(\frac{50 nR}{\gamma - 1}\) | 2. | \(\frac{100 nR}{\gamma - 1}\) |

3. | \(\frac{50 nγR}{\gamma - 1}\) | 4. | \(\frac{25 nγR}{\gamma - 1}\) |

Subtopic: Molar Specific Heat |

81%

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