Mercury, with a coefficient of thermal expansion $\gamma$ , is poured into a thin glass tube, which does not expand on heating. The length of the mercury column is $L.$ If the temperature is raised by $\theta,$ the new length of the mercury column will be:

1. $L(1+\gamma\theta)$ 2. $L\left(1+\dfrac\gamma2\theta\right)$

3. $L\left(1+\dfrac\gamma3\theta\right)$ 4. $L\left(1+\dfrac{2\gamma}3\theta\right)$

Subtopic: Thermal Expansion |

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Q34:

If the temperature (in

$^\circ\text C$ ) of a blackbody is increased

$2$ -fold, then the rate of radiation from the body will become:

1.	$16$ -fold	2.	$4$ -fold
3.	less than $16$ -fold	4.	more than $16$ -fold

Subtopic: Stefan-Boltzmann Law |

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Q32:

Three rods of identical dimensions but made of materials of conductivities

$K,~2K,~K$ are connected in series. The two ends

$A~,B$ are maintained at temperatures of

$0^{\circ} \text{C},~100^{\circ} \text{C}$ respectively. Assume no loss of heat from the sides. The temperatures of the junctions

$X,~Y$ are:

1.

$25^\circ\text C,~75^\circ\text C$
2.

$40^\circ\text C,~60^\circ\text C$
3.

$20^\circ\text C,~80^\circ\text C$
4.

$30^\circ\text C,~70^\circ\text C$

Subtopic: Conduction |

70%

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Q31:

The unit of coefficient of volume expansion of metal is:

1.	$(^\circ\text C)^ {-1}$	2.	$\text{m}^3/^\circ\text C$
3.	$^\circ\text C$	4.	$^\circ\text C/\text{m}^3$

Subtopic: Thermal Expansion |

74%

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Q30:

$200$ g of water at

$20^\circ$ C and

$300$ g of water at

$70^\circ$ C are mixed in a calorimeter of negligible heat capacity. Assume no loss of heat. The final temperature is:
1.

$40^\circ$ C
2.

$50^\circ$ C
3.

$60^\circ$ C
4.

$45^\circ$ C

Subtopic: Calorimetry |

85%

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Q29:

A radiation blackbody has the shape of a sphere of radius

$r.$ Its surface is at a temperature

$T$ (in Kelvin). If the temperature is doubled and the radius is halved, the total rate of radiation emitted from the body:

1.	increases by a factor of $4$
2.	increases by a factor of $2$
3.	remains unchanged
4.	decreases by a factor of $2$

Subtopic: Stefan-Boltzmann Law |

82%

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Q28:

A metallic rod of length

$l$ (at

$0^\circ\text C$ ) expands by

$\Delta l$ when its temperature is increased by

$100^\circ\text C.$ This rod is kept on a surface with its left end maintained at

$0^\circ\text C,$ and its right end at

$100^\circ\text C.$ The rod is insulated along its length, so heat can only be exchanged at the ends. The length of the rod is:

1.	$l+\Delta l$	2.	$l+\dfrac{\Delta l}{2}$
3.	$l+\dfrac{\Delta l}{4}$	4.	$l+\dfrac{3\Delta l}{4}$

Subtopic: Thermal Expansion |

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Q27:

A calorimeter contains

$270$ g of ice at

$0^\circ$ C (specific latent heat

$80$ cal/g). Steam (specific latent heat

$540$ cal/g) at

$100^\circ$ C is continuously passed through it, and the excess steam is allowed to escape. Assume negligible loss of heat to the surroundings, except due to excess steam being allowed to escape. Also, ignore the heat capacity of the calorimeter. The final mass of water in the calorimeter is:
1.

$40$ g
2.

$90$ g
3.

$310$ g
4.

$360$ g

Subtopic: Calorimetry |

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Q26:

Two rods having coefficient of linear expansion

$\alpha,3\alpha$ are connected end-on-end. The average coefficient of thermal expansion for the composite rod:

1.	is $2\alpha$
2.	is $4\alpha$
3.	can be any value between $\alpha$ and $3\alpha$
4.	can be any value between $2\alpha$ and $3\alpha$

Subtopic: Thermal Expansion |

52%

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Q25:

A piece of iron of water equivalent

$10$ g is taken from a furnace and put into a calorimeter containing

$100$ g of water at an initial temperature of

$20^{\circ} \text{C}.$ The final temperature of the system is observed to be

$80^{\circ} \text{C}.$ Ignore the thermal capacity of the calorimeter and any loss of heat. The temperature of the furnace is:
1.

$600^{\circ} \text{C}$
2.

$620^{\circ} \text{C}$
3.

$680^{\circ} \text{C}$
4.

$520^{\circ} \text{C}$

Subtopic: Calorimetry |

62%

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1.	$L(1+\gamma\theta)$	2.	$L\left(1+\dfrac\gamma2\theta\right)$
3.	$L\left(1+\dfrac\gamma3\theta\right)$	4.	$L\left(1+\dfrac{2\gamma}3\theta\right)$

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