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# Thermal Properties of Matter

#### Multiple Choice Questions

1.

Temperature of the star is determined by

• distance

• colour

• size

• none of these

B.

colour

We from Wien's displacement law that

λmT = b,

where

λ=  wavelength of light emitted with maximum intensity

T = temperature of the star

∴ From the colour  ( wavelength ) of the emitted light, we can determine the temperature of the star.

2.

A black body is at a temperature 300 K. It emits energy at a rate, which is proportional to

• 300

• (300)3

• (300)2

• (300)4

D.

(300)4

Temperature of a black body (T) = 300 K.

Stefan's law of radiation states that energy emitted by the black body  (E) is directly proportional to the T4

E ∝ T4 ∝  (300)4

3.

Assertion: Blue star is at high temperature than red star.

Reason: Wein's displacement law states that T  ∝  ( 1/λm ).

• If both the assertion and reason are true and reason is a correct explanation of the assertion.

• If both assertion and reason are but assertion is not a correct explanation of the assertion.

• If the assertion is true but the reason is false.

• If both assertion and reason are false.

A.

If both the assertion and reason are true and reason is a correct explanation of the assertion.

From Wien's displacement law, temperature (T)  ∝ 1/ λm  (where λm is the maximum wavelength). Thus temperature of  a body is inversely proportional to the wavelength. Since blue star has smaller wavelength and red star has maximum wavelength, therefore blue star is at higher temperature then red star.

4.

A constant pressure air thermometer gave a reading 47.5 units of volume when immersed in ice-cold water and 67 units in a boiling liquid. The boiling point of the liquid, is

• 125°C

• 100°C

• 135°C

• 112°C

D.

112°C

Charle's law formula is given in equation (i). This law used to determine the volume or temperature of a gas.

A constant pressure air-thermometer is based on the law

.....(i)

⇒

Here it is given that

V1 = 47.5

V2 = 67

T1 = 0°C = 273 K

∴   T2 = 273  ×  $\frac{67}{47.5}$

= 385.07 K

T2 = 112°C

5.

If hot water is mixed with cold water

• temperature first increases then become constant

• temperature first decreases then become constant

• increases continuously

• first it is uncertain then it become constant

A.

temperature first increases then become constant

When you heat up water, the water molecules start moving around faster and faster. They bounce off each and move farther apart. Because there's more space between the molecules, a volume of hot water has fewer molecules in it and weights a little bit less than the same volume of cold water.

6.

For an enclosure maintained at 1000 K, the maximum radiation occurs at wavelength λm. If the temperature is raised to 2000 K, the peak will shift to

• $\frac{5}{2}{\mathrm{\lambda }}_{\mathrm{m}}$

• $\frac{1}{2}{\mathrm{\lambda }}_{\mathrm{m}}$

• $\frac{7}{2}{\mathrm{\lambda }}_{\mathrm{m}}$

• $\frac{3}{2}{\mathrm{\lambda }}_{\mathrm{m}}$

B.

$\frac{1}{2}{\mathrm{\lambda }}_{\mathrm{m}}$

We know from Wein's displacement law

λmT = constant

∴   λmT1 = λ'm T2

⇒      λ'm

=

⇒      λ'$\frac{{\mathrm{\lambda }}_{\mathrm{m}}}{2}$

7.

According to Wein's displacement law

• λT = constant

• λ/T  = constant

• λ ∝  ( 1/ T2 )

• both (b) and (c)

A.

λT = constant

Wien's displacement law states that the absolute temperature of a black body and the peak wavelength of its radiations are inversely proportional.

λ  ∝ $\frac{1}{\mathrm{T}}$

λT = constant

8.

Assertion:  The earth without its atmosphere would be inhospitably cold.

Reason: All heat would escape in the absence of atmosphere.

• If both the assertion and reason are true and reason is a correct explanation of the assertion.

• If both assertion and reason are true but assertion is not a correct explanation of the assertion.

• If the assertion is true but the reason is false.

• If both assertion and reason are false.

A.

If both the assertion and reason are true and reason is a correct explanation of the assertion.

Heat radiated out by earth is reflected back by the atmosphere. In the absence of atmosphere, all the heat will escape from earth's surface which will make the earth inhospitably cold. The atmosphere helps in maintaining the temperature through convection of heat.

9.

1 Kcal of heat flowing through a rod iron. When the rod is cut down to 4 pieces then what will be the heat flowing through each piece having same differential temperature?

• 1/2 Kcal

• 1/4 Kcal

• 1 Kcal

• 1/15 Kcal

C.

1 Kcal

We know that the heat flowing through  a conductor is given by

⇒      Q = $-$ KA $\left(\frac{\mathrm{d\theta }}{\mathrm{dx}}\right)$t

Where  K = thermal conductivity of the material

A = area of cross-section

t = time

Now if we cut the rod into 4  pieces, A  remains same K remains same, so for same time t, Q is going to be same as earlier.

10.

A solid sphere and a hollow sphere are heated the same temperature. Point out the true statement.

• hollow sphere cools more quickly

• both hollow and solid sphere cools more quickly

• solid sphere cools more quickly

• none of the statement is true

C.

solid sphere cools more quickly

The solid sphere cools more quickly because the thermal conductivity of the solid sphere is more  than that of the hollow sphere.