Thermal Expansion

Q.

At some temperature T, a bronze pin is a little large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when

1. Only the block is heated

2. Both block and pin are heated together

3. Both block and pin are cooled together

4. Only the pin is cooled

Q.

The lengths of steel and copper rods are so that the length of the steel rod is 5 cm longer than that of the copper rod at all temperatures, then length of each rod, are ($\alpha$ for copper = $1.7\times {10}^{-5}{/}^{\circ }C$ and $\alpha$ for steel = $1.1\times {10}^{-5}{/}^{\circ }C$) -

1. 9.08 cm; 14.08 cm

2. 9.50 cm; 14.50 cm

3. 9.17 cm; 14.17 cm

4. 9.02 cm; 14.20 cm

Q.

A bar of iron is 10 cm at 20°C. At 19°C it will be (a of iron = 11 x 10^-6/°C)

1. 11 ´ 10^-5 cm longer

2. 11 ´ 10^-6 cm longer

3. 11 ´ 10^-6 cm shorter

4. 11 ´ 10^-5 cm shorter

Q. If the temperature of a uniform rod is slightly increased by $\Delta t$, its moment of inertia I about a perpendicular bisector increases by -

1. zero

2. αI∆t

3. 3αI∆t

4. 2αI∆t

Q. An iron rod of length 50 cm is joined at an end to an aluminum rod of length 100cm. All measurement refer to ${20}^{\circ }C$. Find the length of the composite system at ${100}^{\circ }C$ and its average coefficient of linear expansion. The coefficient of linear expansion of iron and aluminum are $12\times {10}^{-6}{/}^{\circ }C$ and $24\times {10}^{-6}{/}^{\circ }C$ respectively.

1. 
2. 
3. 
4. 

Q. A clock which keeps correct time at ${25}^{\circ }C$ has a pendulum made of brass whose coefficient of linear expansion is 0.000019. How many seconds a day will it gain if the temperature fall to $0^{\circ }C$.

1. 10.52 sec.
2. 20.52 sec.
3. 220.52 sec.
4. 202 sec.

Q. A clock with a metal pendulum beating seconds keeps correct time at $0^{\circ }C.$ If it loses 12.5 seconds a day at ${25}^{\circ }C,$ the coefficient of linear expansion of metal of pendulum is

1. 
2. 
3. 
4. 

Q. The heat generated by radioactivity within the earth is conducted outward through the oceans. Assuming the average temperature gradient within the solid earth beneath the ocean to be ${0.07}^{\circ }{C}^{-1}$ and the average thermal conductivity $0.2cal{m}^{-1}{s}^{-1}{C}^{-1}$, determine the rate of heat transfer per square meter. Radius of the earth = 6400 km. Further, determine the quantity of heat transferred through the earth's surface each day.

1. 
2. 
3. 
4. 

Q.

Infrared radiation is detected by

1. Pyrometer

2. Nanometer

3. Photometer

4. Spectrometer

Q. Two rods, one of aluminium and the other made of steel, having initial length $l_1$ and $l_2$ are connected together to form a single rod of length $l_1+l_2.$ The coefficients of linear expansion for aluminium and steel are ${\alpha }_a$ and ${\alpha }_a$ and respectively. If the length of each rod increases by the same amount when their temperature are raised by $t^{o}C$, then find the ratio of length of aluminium rod to the whold rod.

(IIT JEE 2003)

1. ${\alpha }_s/{\alpha }_a$
2. ${\alpha }_a/{\alpha }_s$
3. ${\alpha }_s/({\alpha }_a+{\alpha }_s)$
4. ${\alpha }_a/({\alpha }_a+{\alpha }_s)$