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

1. \(P_0V_0+ 2P_0V_0\ln 2\)

2. \(\frac{1}{2}P_0V_0+ 2P_0V_0\ln 2\)

3. \(\frac{5}{2}P_0V_0+ 2P_0V_0\ln 2\)

4. \(3P_0V_0+ 2P_0V_0\ln 2\)

Subtopic: First Law of Thermodynamics |

62%

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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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\(0.04\) mole of an ideal monatomic gas is allowed to expand adiabatically so that its temperature changes from \(800~\text{K}\) to \(500~\text{K}\). 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 \(V_1~\text{and}~V_2\) as shown
in the pressure-temperature \((P\text-T)\) diagram, then:

1. \(V_1= V_2\)

2. \(V_1> V_2\)

3. \(V_1< V_2\)

4. \(V_1\ge V_2\)

Subtopic: Types of Processes |

81%

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In the cyclic process shown in the pressure-volume \((P-V)\) diagram, the change in internal energy is equal to:

1. $\pi {\left(\frac{{\mathrm{P}}_{2}-{\mathrm{P}}_{1}}{2}\right)}^{2}$

2. $\mathrm{\pi}{\left(\frac{{\mathrm{V}}_{2}-{\mathrm{V}}_{1}}{2}\right)}^{2}$

3. $\frac{\mathrm{\pi}}{4}({\mathrm{P}}_{2}-{\mathrm{P}}_{1})({\mathrm{V}}_{2}-{\mathrm{V}}_{1})$

4. zero

Subtopic: Cyclic Process |

73%

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Heat is supplied to a diatomic gas in an isochoric process. The ratio \(\Delta Q:\Delta U\) is: (symbols have usual meanings)

1. \(5:3\)

2. \(5:2\)

3. \(1:1\)

4. \(5:7\)

1. \(5:3\)

2. \(5:2\)

3. \(1:1\)

4. \(5:7\)

Subtopic: First Law of Thermodynamics |

71%

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The pressure-temperature (P-T) graph for two processes, A and B, in a system is shown in the figure. If ${\mathrm{W}}_{1}$ and ${\mathrm{W}}_{2}$ are work done by the gas in process A and B respectively, then:

1. | \(W_{1}\) = \(W_{2}\) | 2. | \(W_{1}\) < \(W_{2}\) |

3. | \(W_{1}\) > \(W_{2}\) | 4. | \(W_{1}\) = \(-W_{2}\) |

Subtopic: Work Done by a Gas |

71%

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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 |

88%

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Work done during the given cycle is:

1. 4${P}_{0}{V}_{0}$

2. 2${P}_{0}{V}_{0}$

3. $\frac{1}{2}$${P}_{0}{V}_{0}$

4. ${P}_{0}{V}_{0}$

Subtopic: Work Done by a Gas |

78%

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The efficiency of an ideal heat engine is less than 100% because of:

1. | the presence of friction. |

2. | the leakage of heat energy. |

3. | unavailability of the sink at zero kelvin. |

4. | All of these |

Subtopic: Carnot Engine |

83%

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