Match the following? Column - I Column - II (a) Ratio of change in time period of a simple pendulum with temperature to its original time period (i) α Δ T (b) Ratio of the value of a length to its scale reading (ii) T (c) Reciprocal of coefficient of volume expansion for an ideal gas of constant pressure (iii) ( 1 + α Δ T ) (d) F Y A = (iv) 1 2 α Δ T

( a − i v ) , ( b − i i i ) , ( c − i i ) , ( d − i )

( a − i v ) , ( b − i i ) , ( c − i ) , ( d − i i )

( a − i i i ) , ( b − i v ) , ( c − i i ) , ( d − i )

( a − i v ) , ( b − i ) , ( c − i i ) , ( d − i i i )

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A hole of diameter $5 cm$ is drilled in a metal sheet at $30 ° C$ . The linear expansion of metal is $2 \times 10^{- 5} K^{- 1}$ . The diameter of the hole when the temperature is raised to $230 ° C$ , is equal to

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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

The three types of expansion that takes place in solid are

EASY

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

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 of Solids, Liquids and Gases

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

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MEDIUM

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

A cylinder has a piston at temperature of

30 ° C

. There is all round clearance of

0.08 mm

between the piston and cylinder wall if internal diameter of the cylinder is

15 cm

. What is the temperature at which piston will fit into the cylinder exactly?

(α_{p} = 1.6 \times 10^{- 5} / {}^{\circ}C

and

α_{c} = 1.2 \times 10^{- 5} / {}^{\circ}C)

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

If two rods of lengths

L

and

2 L,

having coefficients of linear expansion

α

and

2 α

respectively are connected end-to-end, then find the average coefficient of linear expansion of the composite rod.

EASY

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

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

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

Expansion during heating:

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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 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

A glass vessel of volume

V_{0}

is completely filled with a liquid and its temperature is raised by

Δ T

. What volume of the liquid will flow over, if the coefficient of linear expansion of glass is

α_{g}

and coefficient of volume expansion of the liquid is

γ_{L}

EASY

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

The ratio of linear expansivity to the co-efficient of a real expansion of a rectangular sheet of a solid is

MEDIUM

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

An iron ring of radius

2.1 m

is to be fitted on top of the rim of a wheel of radius

2.121 m

. The coefficient of volume expansion for iron is

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

. By approximately how much should the temperature of the iron ring be increased so that it fits the rim of the wheel?

EASY

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

Match the following?

	Column $- I$		Column $- II$
(a)	Ratio of change in time period of a simple pendulum with temperature to its original time period	(i)	$α Δ T$
(b)	Ratio of the value of a length to its scale reading	(ii)	$T$
(c)	Reciprocal of coefficient of volume expansion for an ideal gas of constant pressure	(iii)	$(1 + α Δ T)$
(d)	$\frac{F}{Y A} =$	(iv)	$\frac{1}{2} α Δ T$

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 _____________

EASY

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

For a solid, how many types of thermal expansion coefficients are there?

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:

MEDIUM

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:

HARD

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

A hole of diameter 5 cm is drilled in a metal sheet at 30 °C. The linear expansion of metal is 2×10-5 K-1. The diameter of the hole when the temperature is raised to 230 °C, is equal to

Important Questions on Thermal Properties of Matter

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A hole of diameter $5 cm$ is drilled in a metal sheet at $30 ° C$ . The linear expansion of metal is $2 \times 10^{- 5} K^{- 1}$ . The diameter of the hole when the temperature is raised to $230 ° C$ , is equal to