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The figure shows the \((P\text-V)\) diagram of an ideal gas undergoing a change of state from \(A\) to \(B\). Four different paths \(\mathrm{I, II, III}\) and \(\mathrm{IV}\), as shown in the figure, may lead to the same change of state.

(a) | The change in internal energy is the same in cases \(\mathrm{IV}\) and \(\mathrm{III}\) but not in cases \(\mathrm{I}\) and \(\mathrm{II}\). |

(b) | The change in internal energy is the same in all four cases. |

(c) | Work done is maximum in case \(\mathrm{I}\). |

(d) | Work done is minimum in case \(\mathrm{II}\). |

Which of the following options contains only correct statements?

1. | (b), (c), (d) | 2. | (a), (d) |

3. | (b), (c) | 4. | (a), (c), (d) |

Subtopic: Work Done by a Gas |

79%

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Consider a cycle followed by an engine (figure).

1 to 2 is isothermal,

2 to 3 is adiabatic,

3 to 1 is adiabatic.

Such a process does not exist, because:

(a) | heat is completely converted to mechanical energy in such a process, which is not possible. |

(b) | In this process, mechanical energy is completely converted to heat, which is not possible. |

(c) | curves representing two adiabatic processes don’t intersect. |

(d) | curves representing an adiabatic process and an isothermal process don't intersect. |

Choose the correct alternatives:

1. | (a), (b) | 2. | (a), (c) |

3. | (b), (c) | 4. | (c), (d) |

Subtopic: First Law of Thermodynamics | Second Law of Thermodynamics |

55%

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The pressure and volume of a gas are changed as shown in the P-V diagram. The temperature of the gas will:

1. | increase as it goes from A to B. |

2. | increase as it goes from B to C. |

3. | remain constant during these changes. |

4. | decrease as it goes from D to A. |

Subtopic: Types of Processes |

66%

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Two cylinders contain the same amount of an ideal monoatomic gas. The same amount of heat is given to two cylinders.
If the temperature rise in cylinder A is T_{0}, then the temperature rise in cylinder B will be:

1. $\frac{4}{3}{\mathrm{T}}_{0}$

2. $2{\mathrm{T}}_{0}$

3. $\frac{{\mathrm{T}}_{0}}{2}$

4. $\frac{5}{3}{\mathrm{T}}_{0}$

Subtopic: Molar Specific Heat |

58%

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The incorrect relation is:

(where symbols have their usual meanings)

1. ${\mathrm{C}}_{\mathrm{P}}=\frac{\mathrm{\gamma R}}{\mathrm{\gamma}-1}$

2. ${\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=\mathrm{R}$

3. $\u2206\mathrm{U}=\frac{{\mathrm{P}}_{\mathrm{f}}{\mathrm{V}}_{\mathrm{f}}-{\mathrm{P}}_{\mathrm{i}}{\mathrm{V}}_{\mathrm{i}}}{1-\mathrm{\gamma}}$

4. ${\mathrm{C}}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{\gamma}-1}$

Subtopic: Molar Specific Heat |

81%

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We consider a thermodynamic system. If ∆U represents the increase in its internal energy and W the work done by the system, which of the following statements is true?

1. | \(\Delta \mathrm{U}=-\mathrm{W}\) in an isothermal process |

2. | \(\Delta \mathrm{U}=\mathrm{W}\) in an isothermal process |

3. | \(\Delta \mathrm{U}=-\mathrm{W}\) in an adiabatic process |

4. | \(\Delta \mathrm{U}=\mathrm{W}\) in an adiabatic process |

Subtopic: First Law of Thermodynamics |

83%

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AIPMT - 1998

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Two cylinders, \(A\) and \(B\), of equal capacity are connected to each other via a stopcock. \(A\) contains gas at a standard temperature and pressure. \(B\) is completely evacuated. The entire system is thermally insulated. If the stopcock is suddenly opened, then the change in internal energy of the gas is:

1. \(0\)

2. \(5~\text{J}\)

3. \(1~\text{J}\)

4. \(3~\text{J}\)

1. \(0\)

2. \(5~\text{J}\)

3. \(1~\text{J}\)

4. \(3~\text{J}\)

Subtopic: First Law of Thermodynamics |

88%

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Find out the total heat given to diatomic gas in the process A$\to $B$\to $C : (B$\to $C is isothermal)

1. ${\mathrm{P}}_{0}{\mathrm{V}}_{0}+2{\mathrm{P}}_{0}{\mathrm{V}}_{0}$ $\mathrm{ln}2$

2. $\frac{1}{2}$${\mathrm{P}}_{0}{\mathrm{V}}_{0}+2{\mathrm{P}}_{0}{\mathrm{V}}_{0}\mathrm{ln}2$

3. $\frac{5}{2}$${\mathrm{P}}_{0}{\mathrm{V}}_{0}+2{\mathrm{P}}_{0}{\mathrm{V}}_{0}$ $\mathrm{ln}2$

4. 3${\mathrm{P}}_{0}{\mathrm{V}}_{0}+2{\mathrm{P}}_{0}{\mathrm{V}}_{0}$ $\mathrm{ln}2$

Subtopic: First Law of Thermodynamics |

62%

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0.04 mole of an ideal monatomic gas is allowed to expand adiabatically so that its temperature changes from 800 K to 500 K. The work done during expansion is nearly equal to:

1. | \(129.6\) J | 2. | \(-129.6\) J |

3. | \(149.6\) J | 4. | \(-149.6\) J |

Subtopic: Work Done by a Gas |

57%

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If an ideal gas undergoes two processes at constant volumes ${\mathrm{V}}_{1}$ $\mathrm{and}$ ${\mathrm{V}}_{2}$ as shown in the pressure-temperature (P-T) diagram, then:

1. ${\mathrm{V}}_{1}$ = ${\mathrm{V}}_{2}$

2. ${\mathrm{V}}_{1}$ > ${\mathrm{V}}_{2}$

3. ${\mathrm{V}}_{1}$ < ${\mathrm{V}}_{2}$

4. ${\mathrm{V}}_{1}\ge {\mathrm{V}}_{2}$

Subtopic: Types of Processes |

81%

From NCERT

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