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Area and Volu...

Area and Volume Expansion

Trending Questions

Q.

Write the relation between coefficient of volume expansion and coefficient of linear expansion.

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Q.

A Bakelite beaker has volume capacity of $500 c c$ at $30 ° C$ . When it is partially filled with $V_{m}$ volume ( $30 ° C$ ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $γ_{(b e a k e r)} = 6 \times 10^{- 6} ° C^{- 1}$ and $γ_{(m e r c u r y)} = 1.5 \times 10^{- 4 °} c^{- 1}$ ¹, where $γ$ is the coefficient of volume expansion, then $V_{m} (i n c c)$ is close to

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Q.

On a hot day in Jaipur, an oil trucker loaded 40 kL (kilolitres) of diesel fuel. On his way to Shimla, he encounters a temperature drop of $20^{\circ} C$ , where he stopped and delivered the entire load. How many litres did he deliver? The γ for diesel is $9.50 \times 10^{- 4} /^{\circ} C$ and α for his steel truck is $11 \times 10^{- 6} /^{\circ} C$ . If you find that the volume has decreased, think about who is paying for the "missing” diesel.

39, 810 L
40, 000 L
39, 240 L
40, 126 L

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Q. A thin brass sheet at

10^{\circ} C

and a thin steel sheet at

20^{\circ} C

have same surface area. The common temperature at which both would have the same area is :
Coefficient of areal expension for brass and steel are

{10 \times 10^{- 6}}^{\circ} C^{- 1}

and

{20 \times 10^{- 6}}^{\circ} C^{- 1}

respectively.

$10^{\circ} C$
$20^{\circ} C$
$30^{\circ} C$
$35^{\circ} C$

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Q. Coefficient of linear expansion of brass and steel rods are

α_{1}

and

α_{2}

. Length of brass and steel rods are

l_{1}

and

l_{2}

respectively. If

l_{2} - l_{1}

is maintained same at all temperatures, then find the ratio of

α_{1}

to

α_{2}

.

$\frac{l_{2}}{l_{1}}$
$\frac{l_{1}}{l_{2}}$
$\frac{α_{2}}{l_{1}}$
$\frac{l_{2}}{α_{1}}$

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Q. A metallic bob of weight

100 gm

is suspended in air. If it is immersed in a liquid at temperature of

30^{\circ} C

, it weighs

90 gm

. When the temperature of the liquid is raised to

100^{\circ} C

, it weighs

90.2 gm

. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is

15 \times 10^{- 6} /^{\circ} C

$3 \times 10^{- 5} /^{\circ} C$
$4 \times 10^{- 4} /^{\circ} C$
$3 \times 10^{- 4} /^{\circ} C$
$4 \times 10^{- 5} /^{\circ} C$

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Q. A non-isotropic solid metal cube has coefficient of linear expansion as

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

along the x-axis and

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

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

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

then the value of

C

is

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Q. A vertical glass tube, closed at the bottom, contains a mercury column of length

L_{0}

at

0^{\circ} C

. If

γ

is the coefficient of cubical expansion of mercury

α

the coefficient of linear expansion of glass, the length of the mercury column when the temperature rises to

t^{\circ} C

is (assuming that

t

not more than

100^{\circ} C

)

$L_{t} = L_{0} [1 + (γ - 3 α) t]$
$L_{t} = L_{0} [1 + (γ + 3 α) t]$
$L_{t} = L_{0} [1 + (γ + 2 α) t]$
$L_{t} = L_{0} [1 + (γ - 2 α) t]$

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Q. The volume of a metal sphere increased by

0.24

% when its temperature is raised by

40^{\circ} C

. The coefficient of linear expansion of metal is

$2 \times {10^{- 5}}^{\circ} C^{- 1}$
$4 \times {10^{- 5}}^{\circ} C^{- 1}$
$5 \times {10^{- 5}}^{\circ} C^{- 1}$
$8 \times {10^{- 5}}^{\circ} C^{- 1}$

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Q.

A one-litre flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in the flask? Given the coefficient of linear expansion of glass is $9 \times 10^{- 6}^{\circ} C^{- 1}$ and the coefficient of volume expansion of mercury is $1.8 \times 10^{- 4}^{\circ} C^{- 1}$

$50 c m^{3}$
$100 c m^{3}$
$150 c m^{3}$
$200 c m^{3}$

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Q.

The coefficient of expansion of a crystal in one direction (x-axis) is $2.0 \times 10^{- 6} K^{- 1}$ and that in the other two perpendicular directions (y and z-axes) is $1.6 \times 10^{- 6} K^{- 1},$ What is the coefficient of cubical expansion of the crystal?

$1.6 \times 10^{- 6} K^{- 1}$
$1.8 \times 10^{- 6} K^{- 1}$
$2.0 \times 10^{- 6} K^{- 1}$
$5.2 \times 10^{- 6} K^{- 1}$

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Q. An insulated chamber at a height

h

above the earth’s surface and maintained at

30^{\circ} C

has a clock fitted with an uncompensated pendulum. The maker of the clock for the chamber mistakenly designs it to maintain correct time at

20^{\circ} C

at that height. It is found that if the chamber were brought to earth’s surface the clock in it would click correct time at

30^{\circ} C

. The coefficient of linear expansion of the material of pendulum is (earth’s radius is

R

):

$\frac{R}{5 h}$
$\frac{5 R}{h}$
$\frac{h}{5 R}$
$\frac{h}{20 R}$

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Q.

What is thermal expansion? What are the basic properties of matter that get affected on expansion?

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Q. A glass flask of volume one litre at

0^{\circ} C

is filled, level full of mercury at this temperature. The flask and mercury are now heated to

100^{\circ} C

. Find the amount of mercury that will spill out, if the coefficient of volume expansion of mercury is

1.82 \times 10^{- 4} /^{\circ} C

and the coefficient of linear expansion of glass is

0.1 \times 10^{- 4} /^{\circ} C

respectively.

$21.2 cc$
$15.2 cc$
$1.52 cc$
$2.12 cc$

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Q. A weight thermometer contains 51 gm of mercury at

0^{\circ} C

. When placed in an oil bath 1.0 gm is found to overflow. Find the temperature of oil bath. Coefficient of cubical expansion of mercury and glass are

{0.00018}^{\circ} C

and

{0.000026}^{\circ} C

respectively.

${1290.87}^{\circ} C$
${129.87}^{\circ} C$
${199.87}^{\circ} C$
${19.87}^{\circ} C$

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Q.

A glass flask of volume one litre at $0^{\circ} C$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100^{\circ} C$ . How much mercury will spill out, if coefficient of volume expansion of mercury is 1.82× $10^{- 4} /^{\circ} C$ and linear expansion of glass is 0.1× $10^{- 4} /^{\circ} C$ respectively

21.2 cc
15.2 cc
1.52 cc
2.12 cc

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Q. A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are

γ_{1}

and

γ_{2}

respectively. If their temperature are increased by

Δ T

each, the fraction of the volume of metal submerged in mercury changes by a factor of

$(γ_{2} - γ_{1}) Δ T$
$γ_{1} Δ T$
$(1 + (γ_{2} - γ_{1}) Δ T)$
$\frac{γ_{2}}{γ_{1}}$

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Q. A metal of mass

1 kg

at constant atmospheric pressure and at initial temperature

23^{\circ} C

is given a heat of

10000 J

. Specific heat of the metal is

500 {J /kg}^{\circ} C

, coefficient of cubical expansion

γ = 8 \times 10^{- 5} /^{\circ} C

, density =

4000 {kg/m}^{3}

& atmospheric pressure

= 10^{5} {N/m}^{2}

). Choose the correct statement(s).

Temperature of metal body increases by $20^{\circ} C$ .
Work done by metal against atmosphere is $0.04 J$ .
In this problem, $Δ U = 9999.96 J$ .
None of these

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Q. A glass flask is filled upto a mark with

50 {cm}^{3}

of mercury at

18^{\circ} C

. If the flask and contents are heated to

38^{\circ} C

, how much mercury will be above the mark?

α

for glass is

10 \times {10^{- 6}}^{\circ} C^{- 1}

and coefficient of volumetric expansion of mercury is

180 \times {10^{- 6}}^{\circ} C^{- 1}

$0.25 {cm}^{3}$
$0.5 {cm}^{3}$
$0.35 {cm}^{3}$
$0.15 {cm}^{3}$

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Q.

A tumbler, made purely of iron, can be filled with 500 ml ( $\sim 500 c m^{3}$ ) of water during a spring temperature of $20^{\circ} C$ . How much water (in volume) can you store in the tumbler in autumn, if the temperature drops to $8^{\circ} C$ ? ( $γ F e$ = $33.3$ $/^{\circ} C$ ).

499.8 mL
498.9 mL
501.2 mL
None of these

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Q.

A gas in an airtight container is heated from $25^{\circ} C$ to $90^{\circ} C$ . The density of the gas will:
( Consider there is a negligible expansion of container)

Increase slightly
Increase considerably
Remain the same
Decrease slightly

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Q. An iron rod of length

50 cm

is joined at an end to an aluminium rod of equal length to form a system. All measurements refer to

20^{\circ} C

. If coefficient of linear expansion of iron and aluminium are

12 \times 10^{- 6} /^{\circ} C

and

24 \times 10^{- 6} /^{\circ} C

respectively, find average coefficient of linear expansion of composite system?

$36 \times {10^{- 6}}^{\circ} C$
$20 \times {10^{- 6}}^{\circ} C$
$24 \times {10^{- 6}}^{\circ} C$
$38 \times {10^{- 6}}^{\circ} C$

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Q. A metallic bob of weight

100 gm

is suspended in air. If it is immersed in a liquid at temperature of

30^{\circ} C

, it weighs

90 gm

. When the temperature of the liquid is raised to

100^{\circ} C

, it weighs

90.2 gm

. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is

15 \times 10^{- 6} /^{\circ} C

$3 \times 10^{- 5} /^{\circ} C$
$4 \times 10^{- 4} /^{\circ} C$
$3 \times 10^{- 4} /^{\circ} C$
$4 \times 10^{- 5} /^{\circ} C$

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Q. The coefficient of linear expansion of a crystalline substance in one direction is

2 \times 10^{- 4} /^{\circ} C

and in every direction perpendicular to it is

3 \times 10^{- 4} /^{\circ} C

. The coefficient of cubical expansion of the crystal is equal to

$5 \times 10^{- 4} /^{\circ} C$
$4 \times 10^{- 4} /^{\circ} C$
$8 \times 10^{- 4} /^{\circ} C$
$7 \times 10^{- 4} /^{\circ} C$

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Q. Volume of a cylinder increases by

6 %

upon heating. The area of its curved surface will increase by

$1 %$
$6 %$
$3 %$
$4 %$

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Q. A circular hole in an aluminium plate is 1 cm in diameter at

0^{\circ}

. What is the diameter when the temperature of the plate is raised to

100^{\circ}

. (coefficient of linear expansion of aluminium

α = 2.55 \times 10^{- 5} /^{\circ}

)

$(1.1051)^{1 / 2} c m$
$(10.0051)^{1 / 2} c m$
$(1.51)^{1 / 2} c m$
$(1.0051)^{1 / 2} c m$

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Q.

A gas in an airtight container is heated from $25^{\circ} C$ to $90^{\circ} C$ . The density of the gas will:
( Consider there is a negligible expansion of container)

Increase slightly
Increase considerably
Remain the same
Decrease slightly

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Q.

The coefficient of volumetric expansion of mercury is $8 \times 10^{- 5}^{\circ} C$ . A thermometer bulb has a volume $10^{- 6} m^{3}$ and cross section of stem is $0.004 c m^{2}$ . Assuming that bulb is filled with mercury at $0^{\circ} C$ , then the length of the mercury column at $100^{\circ} C$ is:

$18.8 m m$
$9.2 m m$
$7.4 c m$
$2 c m$

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Q. A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are

γ_{1}

and

γ_{2}

respectively. If their temperature are increased by

Δ T

each, the fraction of the volume of metal submerged in mercury changes by a factor of

$(γ_{2} - γ_{1}) Δ T$
$γ_{1} Δ T$
$(1 + (γ_{2} - γ_{1}) Δ T)$
$\frac{γ_{2}}{γ_{1}}$

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Q. A solid whose volume does not change with temperature floats in a liquid. For two different temperatures

t_{1}

and

t_{2}

of the liquid, fractions

f_{1}

and

f_{2}

of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

$\frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$
$\frac{f_{1} - f_{2}}{f_{1} t_{1} - f_{2} t_{2}}$
$\frac{f_{1} + f_{2}}{f_{2} t_{1} + f_{1} t_{2}}$
$\frac{f_{1} + f_{2}}{f_{1} t_{1} + f_{2} t_{2}}$

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