Thermal Expansion

Q.

A thin copper wire of length $l$ increases its length by 1% when heated from temperature $T_1$ to $T_2$. What is the percentage change in area when a thin copper plate having dimensions $2l\times l$ is heated from $T_1$ to $T_2$?

1. 1%

2. 2%

3. 4%

4. 3%

Q.

The density of gold is 19 g/ cm^3.find the volume of 95g of gold.

Q. A steel rod is 3.000 cm in diameter at ${25}^{\circ }C$. A brass ring has an interior diameter of 2.992 cm at ${25}^{\circ }C$. At what common temperature will the ring just slide on to the rod.
${\alpha }_{steel}=12\times {10}^{-6}{K}^{-1}$ and
${\alpha }_{brass}=18\times {10}^{-6}{K}^{-1}$

1. 
2. 
3. 
4. 

Q.

How to calculate percentage? Give example.

Q. An iron tyre is to be fitted onto a wooden wheel 1.0 m in diameter. The diameter of the tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (Coefficient of volume expansion of iron is $3.6\times {10}^{-5}{/}^{\circ }C$)

1. 
2. 
3. 
4. 

Q.

Name two substances which expand on heating.

Q. Is the density of all elements and compounds (substances) different?

Are there any elements or compounds which have same density.

Q.

An Iron rod and a copper rod lie side by side. As the temperature is changed, the difference in the lengths of the rods remains constant at a value of 10 cm. Find the lengths at $0^{\circ }C$. Coefficients of linear expansion of iron and copper are $1.1\times {10}^{-6}{/}^{\circ }C$ and $1.7\times {10}^{-5}{/}^{\circ }C$ respectively.

1. 38.3 cm, 28.3 cm

2. 48.3 cm, 38.3 cm

3. 58.3 cm, 48.3 cm

4. 28.3 cm, 18.3 cm

Q.

What is thermal expansion? Give one example.

Q.

For the same rise in temperature, which expands more, alcohol or mercury?

Q.

A uniform metal rod of length $L$ and mass $M$ is rotating with an angular speed $\omega$ about an axis passing through one of the ends and perpendicular to the rod. If the temperature increases by $t^{\circ }C,$ then the change in its angular speed is proportional to

1. $\frac{1}{\omega }$

2. $\sqrt{\omega }$

3. $\omega$

4. ${\omega }^2$

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. 9.17 cm; 14.17 cm

2. 9.02 cm; 14.20 cm

3. 9.08 cm; 14.08 cm

4. 9.50 cm; 14.50 cm

Q. When equal volumes of two metals are mixed together the density of mixture is 4kg/m3. When equal masses of the same two metals are mixed together, the mixture density is 3kg/m3. Calculate the density of each metal?

Q. Three rods A, B and C, having identical shape and size, are hinged together at ends to form an equilateral triangle. Rods A and B are made of same material having coefficient of linear thermal expansion a while that of material of rod C is ${\alpha }_2$. By how many kelvin must the system of rods be heated to increase the angle opposite to rod C by $\Delta \theta$.

1. 
2. 
3. 
4. 

Q.

Name two substances which contract on heating.

Q.

At ${40}^{\circ }C$, a brass rod has a length 50 cm and a diameter 3.0 mm. It is joined to a steel rod of the same length and diameter at the same temperature. What is the change in the length of the composite rod when it is heated to ${240}^{\circ }C$? The coefficients of linear expansion of brass and steel are $2.0\times {10}^{-5}{}^{\circ }{C}^{-1}$ and $1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$ respectively.

1. 0.32 cm

2. 0.34 cm

3. 0.30 cm

4. 0.28 cm

Q.

How are the (i) mass, (ii) volume, and (iii) density of a metallic piece affected, if at all, with increase in temperature ?

Q.

Explain the following:

The telephone wires break in winter.

Q.

Give two real-life applications of thermal expansion of solids.

Q.

Heat energy is given to $150g$of water, such that its temperature rises by$20K$. When the same amount of heat energy is given to a liquid X of mass $100g$its temperature rises by$80K$. Calculate

(a) heat energy given to water
(b) the specific heat capacity of liquid X. [Take up heat capacity of water$=4.2J{g}^{-1}{K}^{-1}$ ]

Q.

A steel scale measures the length of a copper rod as L cm when both are at ${20}^{\circ }C$, the calibration temperature for the scale. If the coefficients of linear expansion for steel and copper are ${\alpha }_s$ and ${\alpha }_c$ respectively, what would be the scale reading (in cm) when both are at ${21}^{\circ }C$?

1. $\frac{L(1+{\alpha }_c)}{(1+{\alpha }_s)}$

2. $L\frac{{\alpha }_c}{{\alpha }_s}$

3. $L$

4. $L\frac{{\alpha }_s}{{\alpha }_c}$

Q.

$500\mathrm{g}$ of water at $60°\mathrm{C}$ is contained in a vessel of negligible heat capacity. Into this water is added $400\mathrm{g}$ of ice at $0°\mathrm{C}$. Calculate the amount of ice which does not melt.
[Take $S.H.C$ of water $=4.2\mathrm{J}{\mathrm{g}}^{-1}{{}^{\circ }\mathrm{C}}^{-1}$ and $S.L.H$ of ice $=336{\mathrm{Jg}}^{-1}$ ]

Q.

A solid of mass $25g$(sp. heat capacity $0.8J/g°C$) and at $120°C$ is placed in $100g$of water at $20°C$. Calculate the final temperature of the mixture. Specific heat capacity of water is $4.2J/g^{-1}°C$.

Q. If objects of the same volume displace the same amount of water, the how did Archimedes's gold crown experiment work?

Q. Span of a bridge is 2.4 km. At ${30}^{\circ }C$ a cable along the span sags by 0.5 km. Taking $\alpha =12\times {10}^{-6}pe{r}^{\circ }C,$ change in length of cable for a change in temperature from ${10}^{\circ }Cto{42}^{\circ }C$ is

1. 0.4 km
2. 9.9 m
3. 0.099 m
4. 0.99 m

Q.

Two rods A and B of different materials are welded together as shown in the figure. If their thermal conductivities are $k_1$ and $k_2$, the thermal conductivity of the composite rod will be

1. $\frac{3}{2}(k_1+k_2)$

2. $2(k_1+k_2)$

3. $k_1+k_2$

4. $\frac{1}{2}(k_1+k_2)$

Q.

What percent is :

$5\mathrm{cm}\mathrm{of}1\mathrm{m}$

Q.

Name a liquid metal which is heavier than solid silver.

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

Q. An alloy of gold and silver contains 38.5% sliver by mass and has a density of 14.6 g.mL-1 . What is the molar concentration of sliver in this alloy