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The gases expand much less than solids and liquids for a given increase in temperature.

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Important Questions on Thermal Properties of Matter

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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}

)

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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 _____________

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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:

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

Two different wires having lengths

L_{1}

and

L_{2}

and respective temperature coefficient of linear expansion

α_{1}

and

α_{2},

are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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

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:

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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})

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

A steel rod at

25 ° C

is observed to be

1 m

long when measured by another metal scale which is correct at

0 ° C

. The exact length of steel rod at

0 ° C

(α_{steel} = 12 \times 10^{- 6} ° C^{- 1}, α_{metal} = 20 \times 10^{- 6} ° C^{- 1})

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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:

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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:

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

Two rods of different materials having coefficients of linear expansion

α_{1}, α_{2}

and Young's modulii

Y_{1}

and

Y_{2}

respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If

α_{1} : α_{2} = 2 : 3

, the thermal stresses developed in the two rods are equally provided

Y_{1} : Y_{2}

is equal to

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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

A sphere, a cube and a thin circular plate all of same material and same mass initially heated to same high temperature are allowed to cool down under similar conditions. Then the

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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:

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

The coefficient of linear expansion of crystal in one direction is

α_{1}

and that in every direction perpendicular to it is

α_{2}

. The coefficient of cubical expansion is

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

Two metal plates $P$ and $Q$ of same material are arranged as shown in the figure. If both the plates are uniformly heated through same range of temperature, then

Question Image

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

The area measured on the surface of a solid body of coefficient of linear expansion

α

A_{0}

at some initial temperature. If the temperature changes by

Δ T

, the approximate change in area,

Δ A

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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:

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Thermal Expansion

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

The linear expansion of a solid rod is independent of its:

The gases expand much less than solids and liquids for a given increase in temperature.

Important Questions on Thermal Properties of Matter

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