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Two metal rods made of steel and copper have coefficients of linear expansion $1.1 \times 10^{- 5} K^{- 1}$ and $1.7 \times 10^{- 5} K^{- 1}$ respectively. At room temperature $(300 K)$ , the steel rod is $4 cm$ longer than the copper rod. If the difference in their lengths remains same at all temperatures, then the lengths of the steel and copper rods respectively (at $300 K$ ) are

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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

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:

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

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

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 :

EASY

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

Thermal expansion of a solid is due to the

EASY

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

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

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 _____________

EASY

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

A bimetallic strip consists of metals $A$ and $B$ . It is mounted rigidly as shown. The metal $A$ has higher coefficient of expansion compared to that of metal $B$ . When the bimetallic strip is placed in a cold both, it will :

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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

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)

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

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

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})

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

Each side of a box made of metal sheet in cubic shape is

a

at room temperature

T

, the coefficient of linear expansion of the metal sheet is

α

. The metal sheet is heated uniformly, by a small temperature

Δ T

, so that its new temperature is

T + Δ T

. Calculate the increase in the volume of the metal box.

MEDIUM

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

The densities of wood and benzene at

0 ° C

are

880 kg m^{- 3}

and

900 kg m^{- 3}

, respectively. The coefficients of volume expansion are

1.2 \times 10^{- 3} ° C^{- 1}

for wood and

1.5 \times 10^{- 3} ° C^{- 1}

for benzene. At what temperature will a piece of wood just sink in benzene?

EASY

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

The two-metre scales, one of steel and the other of aluminium agree at

20 ° C

. The ratio of aluminium

(in cm)

to steel

(in cm)

0 ° C

(α

for steel is

1.1 \times 10^{- 5} ° C^{- 1}

and for aluminium is

2.3 \times 10^{- 5} ° C^{- 1})

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

A solid expands upon heating because-

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

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?

Important Questions on Thermal Properties of Matter

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