Thermal Expansion

Q. A surveyor's 30m steel tape is correct at a temperature of ${20}^{\circ }C$. The distance between two points, as measured by this tape on a day when the temperature is ${35}^{\circ }C$, is 26m. What is the true distance between the points? (${\alpha }_{steel}$ = $1.2\times {10}^{-5}{/}^{\circ }C$.)

1. $26.00468m$

2. $25.90201m$
3. $26.35048m$

4. $26m$ (should not change)

Q. A hot body placed in air cooled down according to Newton's law of cooling, the rate of decrease of temperature being k times the temperature difference from the surrounding. Starting from t = 0, find the time in which the body will lose half the maximum heat it can lose.

1. k/ln(2)
2. k ln2
3. $\frac{ln2}{k}$
4. 2 ln(k)

Q.

Discuss the factors on which the amount of expansion depends when a solid is heated.

Q. A pendulum clock consists of an iron rod connected to a small, heavy bob. If it is designed to keep correct time at ${20}^{\circ }C$, how fast or slow will it go in 24 hours at ${40}^{\circ }C$? Coefficient of linear expansion of iron = $1.2\times {10}^{-5}{/}^{\circ }C$.

1. 10.4 seconds faster
2. 10.4 minutes faster
3. 1 minute slower
4. 10.4 seconds slower

Q. A brass scale is graduated at ${10}^{\circ }C$. What is the true length of a zinc rod which measures 60.00 cm on this scale at ${30}^{\circ }C$? Linear expansively of brass = $18\times {10}^{-6}{K}^{-1}$.

1. 60.02 cm
2. 60.2 cm
3. 61.02 cm
4. 60.0002 cm

Q. Two rods A and B of the same metal, but of length $1\text{m}$ and $2\text{m}$ respectively, are heated from $0{}^{\circ }\text{C}$ to $100{}^{\circ }\text{C}$. Then, ___.

1. both A and B elongate the same.
2. A elongates more than B.
3. B elongates more than A.
4. A elongates, but B contracts.

Q. Name the three types of expansion in solid.
[1 mark]

Q.

A cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system -

1. $x$ decreases, $r$ and $d$ increase

2. $x$ and $r$ increase, $d$ decreases

3. $x$, $r$ and $d$ all increase

4. Data insufficient to arrive at a conclusion

Q.

On a winter day the temperature at a place in Himachal Pradesh was$-16°C$. Convert it into degree Fahrenheit $(°F)$

Q.

All solids expand by same amount when heated at same temperature.

1. True
2. False

Q. Two rods of length $l_1$ and $l_2$ are made of materials whose coefficient of linear expansion are ${\alpha }_1$ and ${\alpha }_2$. If difference between two lengths is independent of temperature then

1. $\frac{l_1}{l_2}=\frac{{\alpha }_1}{{\alpha }_2}$
2. $\frac{{\alpha }_1^2}{l_1}=\frac{{\alpha }_2^2}{l_2}$
3. $\frac{l_1}{l_2}=\frac{{\alpha }_2}{{\alpha }_1}$
4. $l_2^2{\alpha }_1=l_1^2{\alpha }_2$

Q. By what temperature a rod should be heated so that it's length becomes $2l_0$ if initial length is $l_0$ . Assume that $alpha$ (coefficient of linear expansion) in that range of temperature remains constant and melting point is very high.

1. $\frac{ln2}{\alpha }$
2. $\frac{ln1}{\alpha }$
3. $\frac{2}{\alpha }$
4. $\frac{1}{\alpha }$

Q.

Why is there a small gap left between the rails while laying the railway tracks?

Q. The coefficient of linear expansion of brass and steel are ${\alpha }_1$ and ${\alpha }_2$. If we take a brass rod of length $l_1$ and steel rod of length $l_2$ at $0^{\circ }C$ and their difference in length ($l_2-l_1$) will remain the same at all temperatures if

1. ${\alpha }_1{l}_2={\alpha }_2{l}_1$
2. ${\alpha }_1{l}_2^2={\alpha }_2{l}_1^2$
3. ${\alpha }_1^2{l}_2={\alpha }_2^2{l}_1$
4. ${\alpha }_1{l}_1={\alpha }_2{l}_2$

Q. The normal density of gold is $\rho$ and its bulk modulus is $K$. The increase in density of a lump of gold, when a pressure $P$ is applied uniformly on all sides is

1. $\frac{\rho P}{K}$
2. $\frac{\rho K}{P}$
3. $\frac{P}{\rho K}$
4. $\frac{K}{\rho P}$

Q. The earth receives solar radiation at a rate of $8.2J/c{m}^2$-minute. Assuming that the sun radiates like a blackbody, calculate the surface temperature of the sun. The angle subtended by the sun on the earth is ${0.53}^{\circ }$ and the Stefan constant
$\sigma =5.67\times {10}^{-8}W/m^2{K}^4$

1. 5000 K
2. 5800 K
3. 5400 K
4. 6200 K

Q.

Infrared radiation is detected by

1. Spectrometer

2. Pyrometer

3. Nanometer

4. Photometer

Q. Four metal cans are identical except for the colour and texture of their outer surfaces. $100c{m}^3$ of water at ${70}^{\circ }C$ is poured into each can. Which can cool most rapidly ?

1. $P$
2. $Q$
3. $R$
4. $S$

Q. A bimetallic strip bends on heating due to:

(a) same expansion
(b) uneven expansion
(c) no expansion
(d) friction

[1 mark]

Q. Two rods of length $l_1$ and $l_2$ are made of materials whose coefficient of linear expansion are ${\alpha }_1$ and ${\alpha }_2$. If difference between two lengths is independent of temperature then

1. $\frac{l_1}{l_2}=\frac{{\alpha }_1}{{\alpha }_2}$
2. $\frac{{\alpha }_1^2}{l_1}=\frac{{\alpha }_2^2}{l_2}$
3. $l_2^2{\alpha }_1=(l_1^2{\alpha }_2$
4. $\frac{l_1}{l_2}=\frac{{\alpha }_2}{{\alpha }_1}$

Q. A glass vessel of volume $100c{m}^3$ is filled with mercury and is heated from ${25}^{\circ }Cto{75}^{\circ }C$. What volume of mercury will overflow? Coefficient of linear expansion of glass $=1.8\times {10}^{-6}{/}^{\circ }C$ and coefficient of volume expansion of mercury is $1.8\times {10}^{-4}{/}^{\circ }C$.

1. $0.87c{m}^3$.
2. $0.67c{m}^3$.
3. $1.74c{m}^3$.
4. $0.98c{m}^3$.

Q.

A pendulum clock keeps correct time at $0^{\circ }$. Its mean coefficient of linear expansions is $\alpha {/}^{\circ }$, then the loss in seconds per day by the clock if the temperature rises by $t^{\circ }$ is

1. $\frac{\frac{1}{2}\alpha t\times 864000}{1-\frac{\alpha t}{2}}$

2. $\frac{1}{2}\alpha t\times 86400$

3. $\frac{\frac{1}{2}\alpha t\times 86400}{{(1-\frac{\alpha t}{2})}^2}$

4. $\frac{\frac{1}{2}\alpha t\times 846400}{1+\frac{\alpha t}{2}}$

Q.

Telephone wires are kept tight between two poles in summer.

1. True
2. False

Q.

Telephone wires _________ during winters.

Q.

Small gaps are left between railway tracks. Give reasons.

Q. Match the following electromagnetic radiations with their sources.

1. Red hot bodies
2. Crystal oscillator
3. Radar communication

Q.

A metal sheet has a circular hole cut out in middle. ​

On application of heat the sheet will undergo thermal expansion. Which image shows correct expansion ?

Q. What do you understand by thermal expansion of a substance?
[ 1 mark ]

Q.

What is the percentage change in length of 1m iron rod if the temperature change by ${100}^{\circ }$C ($\alpha =2\times {10}^{-5}{/}^{\circ }$)C

1. $0.1\%$

2. $0.2\%$

3. $0.3\%$

4. $0.4\%$

Q.

In the given figure, when temperature is increased then which of the following increases.

1. $R_2$

2. All of these

3. $R_1$

4. $R_2-R_1$