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Two conducting slabs of heat conductivity \(K_{1} ~\text{and}~K_{2}\) are joined as shown in figure. If the temperature at the ends of the slabs are \(\theta_{1}~\text{and}~\theta_{2} \ (\theta_{1} > \theta_{2} ), \) then the final temperature \( \left(\theta\right)_{m} \) of the junction will be:

1. | \(\frac{K_{1} \theta_{1} + K_{2} \theta_{2}}{K_{1} + K_{2}}\) | 2. | \(\frac{K_{1} \theta_{2} + K_{2} \theta_{1}}{K_{1} + K_{2}}\) |

3. | \(\frac{K_{1} \theta_{2} + K_{2} \theta_{1}}{K_{1} - K_{2}}\) | 4. | None |

Subtopic: Conduction |

83%

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AIPMT - 1999

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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%

From NCERT

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A piece of iron is heated in a flame. If it becomes dull red first, then becomes reddish yellow, and finally turns to white hot, the correct explanation for the above observation is possible by using:

1. | Stefan's law | 2. | Wien's displacement law |

3. | Kirchhoff's law | 4. | Newton's law of cooling |

Subtopic: Wien's Displacement Law |

81%

From NCERT

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The diagram shows a bimetallic strip used as a thermostat in a circuit. Copper expands more than Invar for the same temperature rise.

What will be switched on when the bimetallic strip becomes hot?

1. | bell only | 2. | lamp and bell only |

3. | motor and bell only | 4. | lamp, bell, and motor |

Subtopic: Thermal Expansion |

From NCERT

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In an experiment on the specific heat of a metal, a \(0.20\) kg block of the metal at \(150^{\circ}\text{C}\) is dropped in a copper calorimeter (of water equivalent of \(0.025\) kg) containing \(150~\text{cm}^{3}\) of water at \(27^{\circ}\text{C}\). The final temperature is \(40^{\circ}\text{C}\). The specific heat of the metal will be:

(Heat losses to the surroundings are negligible)

1. \(0 . 40 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)

2. \(0 . 43 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)

3. \(0 . 54 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)

4. \(0 . 61 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)

Subtopic: Calorimetry |

60%

From NCERT

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A brass wire \(1.8\) m long at \(27\) °C is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of\(-39\) °C, what is the tension created in a wire with a diameter of \(2.0\) mm? (coefficient of linear expansion of brass \(=2.0 \times10^{-5}\) K^{–1}, Young's modulus of brass\(=0.91 \times10^{11}\) Pa)

1. \(3.8 \times 10^3\) N

2. \(3.8 \times 10^2\) N

3. \(2.9 \times 10^{-2}\) N

4. \(2.9 \times 10^{2}\) N

Subtopic: Thermal Stress |

67%

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Two absolute scales \(A \) and \(B,\) have triple points of water defined to be \(200 A\) and \(350 B\). The relationship between \(T_A \) and \(T_B\):

1. \(T_A = {5 \over 7}T_B\)

2. \(T_A = { 4 \over 7}T_B\)

3. \(T_A = { 6 \over 7}T_B\)

4. \(T_A = T_B\)

1. \(T_A = {5 \over 7}T_B\)

2. \(T_A = { 4 \over 7}T_B\)

3. \(T_A = { 6 \over 7}T_B\)

4. \(T_A = T_B\)

Subtopic: Temperature and Heat |

73%

From NCERT

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5 g of water at \(30^{\circ} \mathrm{C}\) and 5 g of ice at \(-20^{\circ} \mathrm{C}\) are mixed together in a calorimeter. The water equivalent of the calorimeter is negligible, and the specific heat and latent heat of ice are 0.5 \(\text{cal/g}^{\circ} \mathrm{C}\) and 80 \(\text{cal/g}\), respectively. The final temperature of the mixture is:

1. | \(0^{\circ} \mathrm{C}\) | 2. | \(-8^{\circ} \mathrm{C}\) |

3. | \(-4^{\circ} \mathrm{C}\) | 4. | \(2^{\circ} \mathrm{C}\) |

Subtopic: Calorimetry |

72%

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Three rods made of the same material, having the same cross-sectional area but different lengths 10 cm, 20 cm and 30 cm are joined as shown. The temperature of the junction will be:-

1. \(10.8^{\circ}\mathrm{C}\)

2. \(14.6^{\circ}\mathrm{C}\)

3. \(16.4^{\circ}\mathrm{C}\)

4. \(18.2^{\circ}\mathrm{C}\)

Subtopic: Conduction |

70%

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Four rods of the same material with different radii \(r\)* *and length \(l\) are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?

1. \(r = \frac{1}{3}~\text{cm}, l = \frac{1}{9}~\text{cm}\)

2. \(r =3~\text{cm}, l =9~\text{cm}\)

3. \(r =4~\text{cm}, l =8~\text{cm}\)

4. \(r =1~\text{cm}, l =1~\text{cm}\)

Subtopic: Conduction |

73%

From NCERT

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