An ideal gas goes from A to B via two processes, l and ll, as shown. If $\u2206{\mathrm{U}}_{1}$ and $\u2206{\mathrm{U}}_{2}$ are the changes in internal energies in processes I and II, respectively, then (\(P:\) pressure, \(V:\) volume)

1. | ∆U_{1} > ∆U_{2} |
2. | ∆U_{1} < ∆U_{2} |

3. | ∆U_{1} = ∆U_{2} |
4. | ∆U_{1} ≤ ∆U_{2} |

Subtopic: Molar Specific Heat |

87%

From NCERT

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The ratio of molar specific heat capacity at constant pressure (\(C_p\)) to that at constant volume (\(C_v\)) varies with temperature (\(T\)) as:

(Assume temperature to be low.)

1. \(T^0\)

2. \(T^{\frac{1}{2}}\)

3. \(T^1\)

4. \(T^{\frac{3}{2}}\)

(Assume temperature to be low.)

1. \(T^0\)

2. \(T^{\frac{1}{2}}\)

3. \(T^1\)

4. \(T^{\frac{3}{2}}\)

Subtopic: Molar Specific Heat |

84%

From NCERT

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If a gas changes volume from 2 litres to 10 litres at a constant temperature of 300K, then the change in its internal energy will be:

1. | 12 J | 2. | 24 J |

3. | 36 J | 4. | 0 J |

Subtopic: Molar Specific Heat |

85%

From NCERT

AIPMT - 1998

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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%

From NCERT

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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%

From NCERT

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In the P-V graph shown for an ideal diatomic gas, the change in the internal energy is:

1. | \(\frac{3}{2}P(V_2-V_1)\) | 2. | \(\frac{5}{2}P(V_2-V_1)\) |

3. | \(\frac{3}{2}P(V_1-V_2)\) | 4. | \(\frac{7}{2}P(V_1-V_2)\) |

Subtopic: Molar Specific Heat |

80%

From NCERT

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If 3 moles of a monoatomic gas do 150 J of work when it expands isobarically, then a change in its internal energy will be:

1. | 100 J | 2. | 225 J |

3. | 400 J | 4. | 450 J |

Subtopic: Molar Specific Heat |

77%

From NCERT

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If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\mathrm{\gamma}$, the change in internal energy of a mass of gas, when the volume changes from V* *to 2V at constant pressure, P* *is:

1. | $\mathrm{R}/\left(\mathrm{\gamma}-1\right)$ | 2. | PV |

3. | $\mathrm{PV}/\left(\mathrm{\gamma}-1\right)$ | 4. | $\mathrm{PV}\left(\mathrm{\gamma}-1\right)$ |

Subtopic: Molar Specific Heat |

80%

From NCERT

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When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is?

1. | \(2 \over 5\) | 2. | \(3 \over 5\) |

3. | \(3 \over 7\) | 4. | \(5 \over 7\) |

Subtopic: Molar Specific Heat |

70%

From NCERT

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The pressure in a monoatomic gas increases linearly from 4 atm to 8 atm when its volume increases from 0.2 m${}^{3}$ to 0.5 m${}^{3}$. The increase in internal energy will be:

1. | 480 kJ | 2. | 550 kJ |

3. | 200 kJ | 4. | 100 kJ |

Subtopic: Molar Specific Heat |

66%

From NCERT

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