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A steel tape \(1\) m long is correctly calibrated for a temperature of \(27^\circ \text{C}\). The length of a steel rod measured by this tape is found to be \(63.0\) cm on a hot day when the temperature is \(45^\circ \text{C}\). What is the actual length of the steel rod on that day?

(Coefficient of linear expansion of steel = \(1.20\times 10^{-5}~\text{K}^{-1}\)).

1. \( 62.485 \) cm

2. \( 60.762 \) cm

3. \( 65.935 \) cm

4. \( 63.013\) cm

Subtopic: Thermal Expansion |

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A large steel wheel is to be fitted onto a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the wheel's central hole has a diameter of 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft?

(Assume the coefficient of linear expansion of the steel to be constant over the required temperature range and \(\alpha\) steel = \(1.20 \times 10^{-5} K^{-1}\))

2. -70°C

3. -69°C

4. -67°C

Subtopic: Thermal Expansion |

51%

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A geyser heats water flowing at the rate of 3.0 liters per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the fuel consumption rate if its heat of combustion is $4.0\times {10}^{4}J/g$?

1. 15.7 g per min

2. 15.10 g per min

3. 14.39 g per min

4. 17.11 g per min

Subtopic: Calorimetry |

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A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C?

(Co-efficient of linear expansion of copper= $1.70\times {10}^{-5}{\mathrm{K}}^{-1}$)

1. 0.0144 cm

2. 0.0234 cm

3. 0.0123 cm

4. 0.0111 cm

Subtopic: Thermal Expansion |

60%

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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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The coefficient of volume expansion of glycerine is \(49\times 10^{-5}\) K^{–1}. What is the fractional change in its density for a \(30^\circ \text{C}\) rise in temperature?

1. \(1.44\times10^{-3}\)

2. \(1.57\times10^{-3}\)

3. \(1.57\times10^{-2}\)

4. \(1.44\times10^{-2}\)

Subtopic: Thermal Expansion |

62%

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A body cools from \(80\) °C to \(50\) °C in \(5\) minutes. The time it takes to cool from \(60\) °C to \(30\) °C is:

(The temperature of the surroundings is \(20\) °C)

1. \(13\) min

2. \(15\) min

3. \(12\) min

4. \(10\) min

Subtopic: Newton's Law of Cooling |

65%

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A brass boiler has a base area of 0.15 ${m}^{2}$ and a thickness of 1.0 cm. It boils water at a rate of 6.0 kg/min when placed on a gas stove. What is the temperature of the part of the flame in contact with the boiler?

(Thermal conductivity of brass = $109J{s}^{-1}{m}^{-1}{K}^{-1}$, the heat of vaporization of water =$2256\times {10}^{3}J/kg$.)

1. 237.98°C

2. 150°C

3. 137.98°C

4. 100°C

Subtopic: Conduction |

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A ‘thermacole’ icebox is a cheap and efficient method for storing small quantities of

cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of

5.0 cm. If 4.0 kg of ice is put in the box, what is the amount of ice remaining after 6 h?

The outside temperature is 45 °C, and the coefficient of thermal conductivity of thermacole is $0.01J{s}^{-1}{m}^{-1}{K}^{-1}.$$\left[Heatoffusionofwater=335\times {10}^{3}Jk{g}^{-1}\right]$

1. 2.9 kg

2. 3.1 kg

3. 3.7 kg

4 4.10 kg

Subtopic: Conduction |

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A child of mass 30 kg running at a temperature of 101°F is given an antipyrin (i.e. medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to 98 °F in 20 min, what is the average rate of extra evaporation caused, by the drug?

[Assume the evaporation mechanism to be the only way by which heat is lost. The mass of the child is 30 kg. The specific heat of the human body is approximately the same as that of water, and the latent heat of evaporation of water at that temperature is about 580 cal ${g}^{-1}$.]

1. 5.81 g/min

2. 4.39 g/min

3. 8.90 g/min

4. 3.05 g/min

Subtopic: Calorimetry |

54%

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