A meter scale made of steel reads accurately at 20 ° C . In a sensitive experiment, distances accurate up to 0 · 055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this meter scale. Coefficient of linear expansion of steel = 11 × 10 − 6 ° C − 1 .

Given that, A meter scale of steel reads accurate at (let) t 1 = 20 ° C . Maximum error in measuring distance of 1 m is 0 .055 mm . i.e., let l = 1 m and Δ l = 0 .055 mm = 55 × 10 - 6 m . Given that, coefficient of linear expansion of steel is, α = 11 × 10 - 6 ° C - 1 Change in length during expansion is, Δ l = l α Δt Substitute the given values in above formula, we get, Δ l = l α Δt ⇒ 55 × 10 - 6 = 1 11 × 10 - 6 Δ t Δ t = 5 ° C ∴ Range of temperature in which the experiment can be performed is, t 1 ± Δ t ∵ ± Δ t = t 2 - t 1 Range = 20 - 5 to 20 + 5 Range 15 ° C to 25 ° C .

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In a Callender's compensated constant pressure air thermometer, the volume of the bulb is $1800 cc$ . When the bulb is kept immersed in a vessel, $200 cc$ of mercury has to be poured out. Calculate the temperature of the vessel.

Important Questions on Heat and Temperature

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 2]>Chapter 1 - Heat and Temperature>EXERCISES>Q 8

A platinum resistance thermometer reads

0^{o}

when its resistance is

80 Ω

and

100^{o}

when its resistance is

90 Ω

. Find the temperature at the platinum scale at which the resistance is

86 Ω

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CONCEPTS OF PHYSICS [VOLUME 2]>Chapter 1 - Heat and Temperature>EXERCISES>Q 9

A resistance thermometer reads

R = 20.0 Ω

27.5 Ω

, and

50.0 Ω

at the ice point

(0^{o} C)

, the steam point

(100^{o} C)

and the zinc point

(420^{o} C)

respectively. Assuming that the resistance varies with temperature as

R_{θ} = R_{0} (1 + αθ + {βθ}^{2})

, find the values of

R_{0}

α

and

β

. Here

θ

represents the temperature on Celsius scale.

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IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 2]>Chapter 1 - Heat and Temperature>EXERCISES>Q 10

A concrete slab has a length of

10 m

on a winter night when the temperature is

0^{o} C

. Find the length of the slab on a summer day when the temperature is

35^{o} C

. The coefficient of linear expansion of concrete is

1 \cdot 0 \times 10^{- 5}^{o} C^{- 1}

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 2]>Chapter 1 - Heat and Temperature>EXERCISES>Q 11

A meter scale made of steel is calibrated at

20^{o} C

to give correct reading. Find the distance between

50 cm

mark and

51 cm

mark if the scale is used at

10^{o} C

. Coefficient of linear expansion of steel is

1 \cdot 1 \times 10^{- 5}^{o} C^{- 1}

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 2]>Chapter 1 - Heat and Temperature>EXERCISES>Q 12

A railway track (made of iron) is laid in winter when the average temperature is

18 ° C

. The track consists of sections of

12.0 m

placed one after the other. How much gap should be left between two such sections so that there is no compression during summer when the maximum temperature goes to

48 ° C

? Coefficient of linear expansion of iron

11 \times 10^{- 6} ° C^{- 1}

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IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 2]>Chapter 1 - Heat and Temperature>EXERCISES>Q 13

A circular hole of diameter

2.00 cm

is made in an aluminum plate at

0 ° C

. What will be the diameter at

100 ° C

α

for aluminum

= 2.3 \times 10^{- 5} ° C^{- 1}

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 2]>Chapter 1 - Heat and Temperature>EXERCISES>Q 15

A meter scale is made up of steel and measures correct length at

16 ° C

. What will be the percentage error if this scale is used (a) on a summer day when the temperature is

46 ° C

and (b) on a winter day when the temperature is

6 ° C

? Coefficient of linear expansion of steel

= 11 \times 10^{- 6} ° C^{- 1}

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 2]>Chapter 1 - Heat and Temperature>EXERCISES>Q 16

A meter scale made of steel reads accurately at

20 ° C

. In a sensitive experiment, distances accurate up to

0 \cdot 055 mm

1 m

are required. Find the range of temperature in which the experiment can be performed with this meter scale. Coefficient of linear expansion of steel

= 11 \times 10^{- 6} ° C^{- 1}

In a Callender's compensated constant pressure air thermometer, the volume of the bulb is 1800 cc. When the bulb is kept immersed in a vessel, 200 cc of mercury has to be poured out. Calculate the temperature of the vessel.

Important Questions on Heat and Temperature

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In a Callender's compensated constant pressure air thermometer, the volume of the bulb is $1800 cc$ . When the bulb is kept immersed in a vessel, $200 cc$ of mercury has to be poured out. Calculate the temperature of the vessel.