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The coefficient of area expansion \(\beta\) of a rectangular sheet of a solid in terms of the coefficient of linear expansion \(\alpha\) is:

1. \(2\alpha\)

2. \(\alpha\)

3. \(3\alpha\)

4. \(\alpha^2\)

Subtopic: Thermal Expansion |

90%

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A blacksmith fixes an iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are \(5.012\) m and \(5.00\) m, respectively at \(27^{\circ}\text{C}.\) To what temperature should the ring be heated so as to fit the rim of the wheel?

\(\left(\text{Given:}~\alpha~\text{for iron}= 1.20 \times 10^{-5}~^\circ{\text{C}^{-1}}\right)\)

1. \(128^{\circ}\text{C}\)

2. \(118^{\circ}\text{C}\)

3. \(227^{\circ}\text{C}\)

4. \(218^{\circ}\text{C}\)

Subtopic: Thermal Expansion |

63%

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A sphere of \(0.047\) kg aluminium is placed for sufficient time in a vessel containing boiling water so that the sphere is at \(100^{\circ}\text{C}\). It is then immediately transferred to a \(0.14\) kg copper calorimeter containing \(0.25\) kg water at \(20^{\circ}\text{C}\). The temperature of water rises and attains a steady-state at \(23^{\circ}\text{C}\). The specific heat capacity of aluminium is:

(Given that: Specific heat capacity of copper calorimeter \(= 0.386\times 10^{3}~\text{J kg}^{-1}\text{K}^{-1}\) and the specific heat capacity of water \(s_w= 4.18\times 10^{3}~\text{J kg}^{-1}\text{K}^{-1})\)

1. \(1.811~\text{kJ kg}^{-1}\text{K}^{-1}\)

2. \(1.911~\text{kJ kg}^{-1}\text{K}^{-1}\)

3. \(0.811~\text{kJ kg}^{-1}\text{K}^{-1}\)

4. \(0.911~\text{kJ kg}^{-1}\text{K}^{-1}\)

Subtopic: Calorimetry |

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When \(0.15\) kg of ice at \(0^\circ \text{C}\) is mixed with \(0.30\) kg of water at \(50^\circ \text{C}\) in a container, the resulting temperature is \(6.7^\circ \text{C}.\)

The heat of fusion of ice is: (\(S_{\text{water}}=4186\) J kg^{–1} K^{–1})

1. \( 3.43 \times 10^4\) Jkg^{–1}

2. \( 3.34 \times 10^4\) Jkg^{–1}

3. \( 3.34 \times 10^5\) Jkg^{–1}

4. \(4.34 \times 10^5\) Jkg^{–1}

Subtopic: Calorimetry |

57%

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The heat required to convert \(3\) kg of ice at \(-12^{\circ}\text{C}\) kept in a calorimeter to steam at \(100^{\circ}\text{C}\) at atmospheric pressure is: (Given, the specific heat capacity of ice \(= 2100~\text{J kg}^{-1}\text{K}^{-1},\) the specific heat capacity of water \(= 4186~\text{J kg}^{-1}\text{K}^{-1},\) the latent heat of fusion of ice \(= 3.35\times 10^{5}~\text{J kg}^{-1}\)${\mathrm{}}^{}$

and the latent heat of steam \(= 2.256\times 10^6~\text{J kg}^{-1}.)\)

1. \(9.1\times 10^{7}~\text{J}\)

2. \(8.1\times 10^{6}~\text{J}\)

3. \(9.1\times 10^{6}~\text{J}\)

4. \(8.1\times 10^{7}~\text{J}\)

and the latent heat of steam \(= 2.256\times 10^6~\text{J kg}^{-1}.)\)

1. \(9.1\times 10^{7}~\text{J}\)

2. \(8.1\times 10^{6}~\text{J}\)

3. \(9.1\times 10^{6}~\text{J}\)

4. \(8.1\times 10^{7}~\text{J}\)

Subtopic: Calorimetry |

62%

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What is the temperature of the steel-copper junction in the steady-state of the system shown in the figure? The length of the steel rod = \(15.0\) cm, length of the copper rod = \(10.0\) cm, temperature of the furnace = \(300^{\circ}\text{C}\), temperature of the other end = \(0^{\circ}\text{C}\). The area of the cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel = \(50.2 ~\text{J s}^{-1}\text{m}^{-1}\text{K}^{-1};\) and of copper \(= 385~\text{J s}^{-1}\text{m}^{-1}\text{K}^{-1})\).

1. \(44.4^{\circ}\text{C}\)

2. \(44.4~\text{K}\)

3. \(54.4^{\circ}\text{C}\)

4. \(54.4~\text{K}\)

Subtopic: Conduction |

56%

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An iron bar \(\left(L_{1} = 0 . 1 m , A_{1} = 0 . 02 m^{2} , K_{1} = 79 W m^{- 1} K^{- 1}\right)\) and a brass bar \(\left(L_{2} = 0 . 1 m , A_{2} = 0 . 02 m^{2} , K_{2} = 109 W m^{- 1} K^{- 1}\right)\) are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at 373 K and 273 K respectively. The temperature of the junction of the two bars is:

1. 215 K

2. 315 K

3. 415 K

4.115 K

Subtopic: Conduction |

78%

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A pan filled with hot food cools in \(2\) minutes from \(94^{\circ}\text{C}\) to \(86^{\circ}\text{C}\) when the room temperature is \(20^{\circ}\text{C}\). How long will it take to cool from \(71^{\circ}\text{C}\) to \(69^{\circ}\text{C}\)?

1. \(50\) sec

2. \(52\) sec

3. \(42\) sec

4. \(48\) sec

1. \(50\) sec

2. \(52\) sec

3. \(42\) sec

4. \(48\) sec

Subtopic: Newton's Law of Cooling |

78%

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An iron bar \(K_1 = 79~\text{W m}^{-1}\text{K}^{-1}\) and a brass bar \(K_2 = 109~\text{W m}^{-1}\text{K}^{-1}\) are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at \(373\) K and \(273\) K respectively. Then the equivalent thermal conductivity of the compound bar is:

1. \(94.6~\text{W m}^{-1}\text{K}^{-1}\)

2. \(93.6~\text{W m}^{-1}\text{K}^{-1}\)

3. \(81.6~\text{W m}^{-1}\text{K}^{-1}\)

4. \(91.6~\text{W m}^{-1}\text{K}^{-1}\)

Subtopic: Conduction |

62%

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An iron bar \(\left(L_{1} = 0 . 1 ~ \text{m}, A_{1} = 0 . 02 ~\text{m}^{2}, K_{1} = 79~\text{W m}^{- 1} \text{K}^{- 1}\right)\) and a brass bar \(\left(L_{2}= 0 . 1 ~\text{m}, A_2 = 0.02~\text{m}^2, K_2 = 109~\text{W m}^{-1}\text{K}^{-1}\right)\) are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at \(373\) K and \(273\) K respectively. The heat current through the compound bar is:

1. \(916.1\) W

2. \(826.1\) W

3. \(926.1\) W

4. \(726\) W

Subtopic: Conduction |

62%

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