The figure shows three temperature scales with the freezing and boiling points of water indicated. ( a ) Rank the size of a degree on these scales, greatest first. ( b ) Rank the following temperatures, highest first : 50 º X , 50 º W and 50 º Y .

Since, the given scales X , W , Y are not specified whether they are Celsius/Kelvin/Fahrenheit/Reaumur scale but the boiling and freezing point of water is given in these unspecified temperature scales also we know the boiling and freezing point of water in known scales like Celsius/Kelvin/Fahrenheit scales. (a ) So now, let's take ° C as a reference scale; We know, water has the B.P = 100 ° C and F.P = 0 ° C So, we have; For X ; 100 - 0 ° C = 70 - ( - 20 ) = 90 ° X ⇒ 1 ° C = 9 10 ° X , For W ; 100 - 0 ° C = 120 - 30 = 90 ° W ⇒ 1 ° C = 9 10 ° W , For Y ; 100 - 0 ° C = 90 - 0 = 90 ° Y ⇒ 1 ° C = 9 10 ° Y , As we find that 1 ° C = 9 10 ° ( each of X , W , Y scale ) or we can write 1 ° X = 1 ° W = 1 ° Y = 10 9 ° C , Hence, the size of a degree on these scales are equal. (b) For X scale ; 50 - ( - 20 ) C 1 - 0 = 10 9 ⇒ C 1 = 63 ° C , For W scale ; 50 - 30 C 2 - 0 = 10 9 ⇒ C 2 = 18 ° C , For Y ; 50 - 0 C 3 - 0 = 10 9 ⇒ C 3 = 45 ° C , So, we find that C 1 > C 3 > C 2 Hence, the required order is 50 ° X > 50 ° Y > 50 ° W .

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We have a hollow sphere and a solid sphere of equal radii and of the same material. They are heated to raise their temperature by equal amounts. How will the change in their volumes, due to volume expansions, be related? Consider two cases

$(i)$ hollow sphere is filled with air,

$(ii)$ there is vacuum inside the hollow sphere.

Important Questions on Thermal Properties of Matter

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Alpha Question Bank for Engineering: Physics>Chapter 15 - Thermal Properties of Matter>Exercise - 1>Q 10

What should be the sum of lengths of an aluminium and steel rod at

0 ° C

is, so that at all temperatures their difference in length is

0.25 m .

(Take coefficient of linear expansion for aluminium and steel at

0 ° C

22 \times 10^{- 6} ° C^{- 1}

and

11 \times 10^{- 6} ° C^{- 1}

respectively.)

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Alpha Question Bank for Engineering: Physics>Chapter 15 - Thermal Properties of Matter>Exercise - 1>Q 11

A steel tape is correctly calibrated at

20 ° C

and is used to measure the length of a table at

30 ° C .

Find the percentage error in the measurement of length.

[α_{steel} = 11 \times 10^{- 6} ° C^{- 1}]

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Alpha Question Bank for Engineering: Physics>Chapter 15 - Thermal Properties of Matter>Exercise - 1>Q 12

The figure shows three temperature scales with the freezing and boiling points of water indicated.

Question Image

$(a)$ Rank the size of a degree on these scales, greatest first.

$(b)$ Rank the following temperatures, highest first : $50 º X, 50 º W and 50 º Y .$

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Alpha Question Bank for Engineering: Physics>Chapter 15 - Thermal Properties of Matter>Exercise - 1>Q 13

What is the temperature at which we get the same reading on both the centigrade and Fahrenheit scales?

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Alpha Question Bank for Engineering: Physics>Chapter 15 - Thermal Properties of Matter>Exercise - 1>Q 14

A small quantity of mass

m

of water at a temperature

θ (

{}^{\circ}C)

is poured on to a large mass

M

of ice which is at its melting point. If

c

is the specific heat capacity of water and

L

the latent heat of fusion of ice, then the mass of ice melted is given by,

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Alpha Question Bank for Engineering: Physics>Chapter 15 - Thermal Properties of Matter>Exercise - 1>Q 15

A thermally isolated vessel contains $100 g$ of water at $0 ° C$ . When the air above the water is pumped out, some water freezes and some evaporates at $0 ° C$ itself. Then the mass of the ice formed if no water is left in the vessel. Latent heat of vaporization of water at $0 ° C = 2.10 \times 10^{6} J {kg}^{- 1}$ and latent heat of fusion of ice $= 3.36 \times 10^{5} J {kg}^{- 1}$ .

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Alpha Question Bank for Engineering: Physics>Chapter 15 - Thermal Properties of Matter>Exercise - 1>Q 16

20 gm

ice at

- 10 º C

is mixed with

m gm

steam at

100 º C

. Minimum value of

m

so that finally all ice and steam converts into water.

(s_{ice} = 0.5 cal {gm}^{- 1} º C^{- 1}, s_{water} = 1 cal {gm}^{- 1} º C^{- 1}, L (melting) = 80 cal {gm}^{- 1}

and

L (vaporization) = 540 cal {gm}^{- 1})

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Alpha Question Bank for Engineering: Physics>Chapter 15 - Thermal Properties of Matter>Exercise - 1>Q 17

2 kg

ice at

- 20 º C

is mixed with

5 kg

water at

20 º C .

Then final amount of water in the mixture will be :

[Specific heat of ice = 0.5 cal {gm}^{- 1} º C^{- 1}, Specific heat of water = 1 cal {gm}^{- 1} º C^{- 1}, Latent heat of fusion of ice = 80 cal {gm}^{- 1}]

Important Questions on Thermal Properties of Matter

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