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A wire is made by attaching two segments together end to end. One segment is made of aluminium and the other is steel. The effective coefficient of linear expansion of the two segment wire is $19 \times 10^{- 6} ° C^{- 1}$ . The fraction length of aluminium is $\frac{x}{11}$ then find $x$ . (linear coefficients of thermal expansion of aluminium and steel are $23 \times 10^{- 6} ° C^{- 1}$ and $12 \times 10^{- 6} ° C^{- 1}$ respectively)

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Important Questions on Thermal Properties of Matter

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A solid expands upon heating because-

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A compressive force,

F

is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by

Δ T

. The net change in its length is zero. Let

l

be the length of the rod, A its area of cross-section,

Y

its Young's modulus, and

α

its coefficient of linear expansion. Then,

F

is equal to:

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

Consider two thermometers,

T_{1}

and

T_{2}

of equal length which can be used to measure temperature over the range

θ_{1}

θ_{2} . T_{1}

, contains mercury as a thermometric liquid while

T_{2}

contains bromine. The volumes of the two liquids are the same at the temperature,

θ_{1}

. The volumetric coefficients of expansion of mercury and bromine are

18 \times 10^{- 5} K^{- 1}

and

108 \times 10^{- 5} K^{- 1}

, respectively. The increase in the length of each liquid is the same for the same increase in temperature. If the diameters of the capillary tubes of the two thermometers are

d_{1}

and

d_{2}

respectively, then the ratio

d_{1} : d_{2}

would be closest to:

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A non-isotropic solid metal cube has coefficients of linear expansion as:

5 \times 10^{- 5} /^{o} C

along the x-axis and

5 \times 10^{- 6} /^{o} C

along the y and the z-axis. If the coefficient of volume expansion of the solid is

C \times 10^{- 6} /^{o} C

, then the value of

C

is _____________

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of

1 m

10 ° C .

Now the end P is maintained at

10 ° C,

while the end S is heated and maintained at

400 ° C .

The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is

1.2 \times 10^{- 5} K^{- 1},

the change in length of the wire PQ is

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A simple pendulum made of a bob of mass m and a metallic wire of a negligible mass has a time period of

2 s

T = 0 ° C

. If the temperature of the wire is increased, and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope

S

. If the coefficient of linear expansion of metal is

α

, then the value of

S

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A horizontal steel railroad track has a length of

100 m

when the temperature is

25 ° C .

The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is

40 ° C,

is (Note: The linear coefficient of thermal expansion for steel is

1.1 \times 10^{- 5} / {}^{\circ}C

and the Young's modulus of steel is

(2 \times 10^{11} Pa)

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A leak proof cylinder of length

1 m,

made of a metal which has very low coefficient of expansion is floating vertically in water at

0^{o} C

such that its height above the water surface is

20 c m .

When the temperature of water is increased to

4^{o} C,

the height of the cylinder above the water surface becomes

21 c m .

The density of water at

T = 4^{o} C,

relative to the density at

T = 0^{o} C

is close to:

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

The value of coefficient of volume expansion of glycerin is

5 \times 10^{- 4} K^{- 1}

. The magnitude of fractional change in the density of glycerin for a rise of

40^{o} C

in its temperature is:

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

The pressure that has to be applied to the ends of a steel wire of length

10 cm

to keep its length constant when its temperature is raised by

100 ° C

is :
(For steel, Young's modulus is

2 \times 10^{11} N m^{- 2}

and coefficient of thermal expansion is

1.1 \times 10^{- 5} K^{- 1}

)

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A copper rod of

88 c m

and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of aluminum rod is

(α_{C u} = 1.7 \times 10^{- 5} K^{- 1} a n d α_{Al} = 2.2 \times 10^{- 5} K^{- 1})

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is

20 m s^{- 2}

at a distance of

5 m

from mean position. The time period of oscillation is

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A uniform cylindrical rod of length

L

and radius r, is made from a material whose Young’s modulus of Elasticity equals

Y .

When this rod is heated by temperature T and simultaneously subjected to a net longutudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A pendulum clock loses 12 s a day if the temperature is

40^{o}

C and gains 4s a day if the temperature is

20^{o}

C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion

(α)

of the metal of the pendulum shaft are respectively:

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

40 ° C,

a brass wire of

1 m m

radius is hung from the ceiling. A small mass,

M

is hung from the free end of the wire. When the wire is cooled down from

40 ° C

20 ° C

it regains its original length of

0.2 m .

The value of

M

is close to:
(Coefficient of linear expansion and Young’s modulus of brass are

10^{- 5} /^{°} C

and

10^{11} N / m^{2},

respectively;

g = 10 m s^{- 2}

)

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A Bakelite beaker has volume capacity of

500 cc

30 ° C

. When it is partially filled with

V_{m}

volume (at

30 ° C

) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If

γ_{beaker} = 6 \times 10^{- 6} ° C^{- 1}, γ_{mercury} = 1.5 \times 10^{- 4} ° C^{- 1},

where

γ

is the coefficient of volume expansion, then

V_{m}

(in

cc

) is close to

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

When the temperature of a metal wire is increased from $0 º C to 10 º C$ , its length increases by $0.02 %$ .The percentage change in its mass density will be closed to:

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

Thermal expansion of a solid is due to the

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Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

Coefficient of linear expansion of brass and steel rods are

α_{1}

and

α_{2}

. Lengths of brass and steel rods are

l_{1}

and

l_{2}

, respectively. If

(l_{2} - l_{1})

is maintained the same at all temperatures, which one of the following relations holds good?

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion of Solids, Liquids and Gases

A rod, of length

L

at room temperature and uniform area of cross section

A,

is made of a metal having coefficient of linear expansion

α / ° C

It is observed that an external compressive force

F

is applied on each of its ends, prevents any change in the length of the rod when its temperature rises by

∆ T K

Young's modulus,

Y

for this metal is:

Important Questions on Thermal Properties of Matter

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