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PHXI11:THERMAL PROPERTIES OF MATTER

366423 A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_{1}$ and $K_{2}$ . The equivalent conductivity of the combination is

1

\frac{K_{1} + K_{2}}{2}

2

K_{1} + K_{2}

3

\frac{K_{1} + K_{2}}{2 K_{1} K_{2}}

4

\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}

Explanation:

In parallel combination equivalent thermal resistance is
$\begin{aligned} \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \\ \frac{K (A_{1} + A_{2})}{l} = \frac{K_{1} A_{1}}{l} + \frac{K_{2} A_{2}}{l} \\ K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2} [As A_{1} = A_{2}] . \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366424 Two metallic blocks $M_{1}$ and $M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_{2}$ is $K$ then the thermal conductivity of $M_{1}$ will be : [Assume steady state heat conduction]
supporting img

1

10 K

2

8 K

3

12.5 K

4

2 K

Explanation:

The rate of transfer of heat
$\frac{Δ Q}{Δ t} = K A (\frac{Δ T}{l})$
$\frac{Δ T_{1}}{Δ T_{2}} = \frac{ℓ_{1}}{K_{1}} \times \frac{K_{2}}{l_{2}} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\frac{20}{80} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\Rightarrow K_{1} = 8 K$
Note: Here $K$ is not kelvin.

JEE - 2022

PHXI11:THERMAL PROPERTIES OF MATTER

366425 I.
Gases are poor thermal conductors.
II.
Liquids have conductivities intermediate between solids and gases.
III.
Heat conduction can take place from cold body to hotter body.
Which of the following statement(s) is/are correct?

1 Only I

2 Only II

3 Only III

4 Both I and II

PHXI11:THERMAL PROPERTIES OF MATTER

366426 Assertion :
If thermal conductivity of a rod is 5 , then its thermal resistivity is 0.2 .
Reason :
Thermal conductivity
$= \frac{1}{thermal resistivity}$

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$\begin{aligned} Thermal Conductivity & = \frac{1}{themal resistivity} \\ = \frac{1}{0.2} = 5 \end{aligned}$
So option (1) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366427 The thickness of a metallic plate is $0.4 c m$ . The temperature between its two surface is $20^{\circ} C$ . The quantity of heat flowing per second is 50 $c a l$ from $5 c m^{2}$ area. In $C G S$ system, the coefficient of thermal conductivity will be

1 0.4

2 0.6

3 0.2

4 0.5

Explanation:

$\frac{Q}{t} = \frac{K A (Δ θ)}{l} \Rightarrow 50 = \frac{5 \times 20 K}{0.4}$
$\Rightarrow K = \frac{1}{5} = 0.2$

PHXI11:THERMAL PROPERTIES OF MATTER

366423 A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_{1}$ and $K_{2}$ . The equivalent conductivity of the combination is

1

\frac{K_{1} + K_{2}}{2}

2

K_{1} + K_{2}

3

\frac{K_{1} + K_{2}}{2 K_{1} K_{2}}

4

\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}

Explanation:

In parallel combination equivalent thermal resistance is
$\begin{aligned} \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \\ \frac{K (A_{1} + A_{2})}{l} = \frac{K_{1} A_{1}}{l} + \frac{K_{2} A_{2}}{l} \\ K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2} [As A_{1} = A_{2}] . \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366424 Two metallic blocks $M_{1}$ and $M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_{2}$ is $K$ then the thermal conductivity of $M_{1}$ will be : [Assume steady state heat conduction]
supporting img

1

10 K

2

8 K

3

12.5 K

4

2 K

Explanation:

The rate of transfer of heat
$\frac{Δ Q}{Δ t} = K A (\frac{Δ T}{l})$
$\frac{Δ T_{1}}{Δ T_{2}} = \frac{ℓ_{1}}{K_{1}} \times \frac{K_{2}}{l_{2}} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\frac{20}{80} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\Rightarrow K_{1} = 8 K$
Note: Here $K$ is not kelvin.

JEE - 2022

PHXI11:THERMAL PROPERTIES OF MATTER

366425 I.
Gases are poor thermal conductors.
II.
Liquids have conductivities intermediate between solids and gases.
III.
Heat conduction can take place from cold body to hotter body.
Which of the following statement(s) is/are correct?

1 Only I

2 Only II

3 Only III

4 Both I and II

PHXI11:THERMAL PROPERTIES OF MATTER

366426 Assertion :
If thermal conductivity of a rod is 5 , then its thermal resistivity is 0.2 .
Reason :
Thermal conductivity
$= \frac{1}{thermal resistivity}$

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$\begin{aligned} Thermal Conductivity & = \frac{1}{themal resistivity} \\ = \frac{1}{0.2} = 5 \end{aligned}$
So option (1) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366427 The thickness of a metallic plate is $0.4 c m$ . The temperature between its two surface is $20^{\circ} C$ . The quantity of heat flowing per second is 50 $c a l$ from $5 c m^{2}$ area. In $C G S$ system, the coefficient of thermal conductivity will be

1 0.4

2 0.6

3 0.2

4 0.5

Explanation:

$\frac{Q}{t} = \frac{K A (Δ θ)}{l} \Rightarrow 50 = \frac{5 \times 20 K}{0.4}$
$\Rightarrow K = \frac{1}{5} = 0.2$

PHXI11:THERMAL PROPERTIES OF MATTER

366423 A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_{1}$ and $K_{2}$ . The equivalent conductivity of the combination is

1

\frac{K_{1} + K_{2}}{2}

2

K_{1} + K_{2}

3

\frac{K_{1} + K_{2}}{2 K_{1} K_{2}}

4

\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}

Explanation:

In parallel combination equivalent thermal resistance is
$\begin{aligned} \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \\ \frac{K (A_{1} + A_{2})}{l} = \frac{K_{1} A_{1}}{l} + \frac{K_{2} A_{2}}{l} \\ K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2} [As A_{1} = A_{2}] . \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366424 Two metallic blocks $M_{1}$ and $M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_{2}$ is $K$ then the thermal conductivity of $M_{1}$ will be : [Assume steady state heat conduction]
supporting img

1

10 K

2

8 K

3

12.5 K

4

2 K

Explanation:

The rate of transfer of heat
$\frac{Δ Q}{Δ t} = K A (\frac{Δ T}{l})$
$\frac{Δ T_{1}}{Δ T_{2}} = \frac{ℓ_{1}}{K_{1}} \times \frac{K_{2}}{l_{2}} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\frac{20}{80} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\Rightarrow K_{1} = 8 K$
Note: Here $K$ is not kelvin.

JEE - 2022

PHXI11:THERMAL PROPERTIES OF MATTER

366425 I.
Gases are poor thermal conductors.
II.
Liquids have conductivities intermediate between solids and gases.
III.
Heat conduction can take place from cold body to hotter body.
Which of the following statement(s) is/are correct?

1 Only I

2 Only II

3 Only III

4 Both I and II

PHXI11:THERMAL PROPERTIES OF MATTER

366426 Assertion :
If thermal conductivity of a rod is 5 , then its thermal resistivity is 0.2 .
Reason :
Thermal conductivity
$= \frac{1}{thermal resistivity}$

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$\begin{aligned} Thermal Conductivity & = \frac{1}{themal resistivity} \\ = \frac{1}{0.2} = 5 \end{aligned}$
So option (1) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366427 The thickness of a metallic plate is $0.4 c m$ . The temperature between its two surface is $20^{\circ} C$ . The quantity of heat flowing per second is 50 $c a l$ from $5 c m^{2}$ area. In $C G S$ system, the coefficient of thermal conductivity will be

1 0.4

2 0.6

3 0.2

4 0.5

Explanation:

$\frac{Q}{t} = \frac{K A (Δ θ)}{l} \Rightarrow 50 = \frac{5 \times 20 K}{0.4}$
$\Rightarrow K = \frac{1}{5} = 0.2$

PHXI11:THERMAL PROPERTIES OF MATTER

366423 A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_{1}$ and $K_{2}$ . The equivalent conductivity of the combination is

1

\frac{K_{1} + K_{2}}{2}

2

K_{1} + K_{2}

3

\frac{K_{1} + K_{2}}{2 K_{1} K_{2}}

4

\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}

Explanation:

In parallel combination equivalent thermal resistance is
$\begin{aligned} \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \\ \frac{K (A_{1} + A_{2})}{l} = \frac{K_{1} A_{1}}{l} + \frac{K_{2} A_{2}}{l} \\ K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2} [As A_{1} = A_{2}] . \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366424 Two metallic blocks $M_{1}$ and $M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_{2}$ is $K$ then the thermal conductivity of $M_{1}$ will be : [Assume steady state heat conduction]
supporting img

1

10 K

2

8 K

3

12.5 K

4

2 K

Explanation:

The rate of transfer of heat
$\frac{Δ Q}{Δ t} = K A (\frac{Δ T}{l})$
$\frac{Δ T_{1}}{Δ T_{2}} = \frac{ℓ_{1}}{K_{1}} \times \frac{K_{2}}{l_{2}} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\frac{20}{80} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\Rightarrow K_{1} = 8 K$
Note: Here $K$ is not kelvin.

JEE - 2022

PHXI11:THERMAL PROPERTIES OF MATTER

366425 I.
Gases are poor thermal conductors.
II.
Liquids have conductivities intermediate between solids and gases.
III.
Heat conduction can take place from cold body to hotter body.
Which of the following statement(s) is/are correct?

1 Only I

2 Only II

3 Only III

4 Both I and II

PHXI11:THERMAL PROPERTIES OF MATTER

366426 Assertion :
If thermal conductivity of a rod is 5 , then its thermal resistivity is 0.2 .
Reason :
Thermal conductivity
$= \frac{1}{thermal resistivity}$

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$\begin{aligned} Thermal Conductivity & = \frac{1}{themal resistivity} \\ = \frac{1}{0.2} = 5 \end{aligned}$
So option (1) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366427 The thickness of a metallic plate is $0.4 c m$ . The temperature between its two surface is $20^{\circ} C$ . The quantity of heat flowing per second is 50 $c a l$ from $5 c m^{2}$ area. In $C G S$ system, the coefficient of thermal conductivity will be

1 0.4

2 0.6

3 0.2

4 0.5

Explanation:

$\frac{Q}{t} = \frac{K A (Δ θ)}{l} \Rightarrow 50 = \frac{5 \times 20 K}{0.4}$
$\Rightarrow K = \frac{1}{5} = 0.2$

PHXI11:THERMAL PROPERTIES OF MATTER

366423 A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_{1}$ and $K_{2}$ . The equivalent conductivity of the combination is

1

\frac{K_{1} + K_{2}}{2}

2

K_{1} + K_{2}

3

\frac{K_{1} + K_{2}}{2 K_{1} K_{2}}

4

\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}

Explanation:

In parallel combination equivalent thermal resistance is
$\begin{aligned} \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \\ \frac{K (A_{1} + A_{2})}{l} = \frac{K_{1} A_{1}}{l} + \frac{K_{2} A_{2}}{l} \\ K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2} [As A_{1} = A_{2}] . \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366424 Two metallic blocks $M_{1}$ and $M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_{2}$ is $K$ then the thermal conductivity of $M_{1}$ will be : [Assume steady state heat conduction]
supporting img

1

10 K

2

8 K

3

12.5 K

4

2 K

Explanation:

The rate of transfer of heat
$\frac{Δ Q}{Δ t} = K A (\frac{Δ T}{l})$
$\frac{Δ T_{1}}{Δ T_{2}} = \frac{ℓ_{1}}{K_{1}} \times \frac{K_{2}}{l_{2}} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\frac{20}{80} = \frac{16}{K_{1}} \times \frac{K}{8}$
$\Rightarrow K_{1} = 8 K$
Note: Here $K$ is not kelvin.

JEE - 2022

PHXI11:THERMAL PROPERTIES OF MATTER

366425 I.
Gases are poor thermal conductors.
II.
Liquids have conductivities intermediate between solids and gases.
III.
Heat conduction can take place from cold body to hotter body.
Which of the following statement(s) is/are correct?

1 Only I

2 Only II

3 Only III

4 Both I and II

PHXI11:THERMAL PROPERTIES OF MATTER

366426 Assertion :
If thermal conductivity of a rod is 5 , then its thermal resistivity is 0.2 .
Reason :
Thermal conductivity
$= \frac{1}{thermal resistivity}$

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$\begin{aligned} Thermal Conductivity & = \frac{1}{themal resistivity} \\ = \frac{1}{0.2} = 5 \end{aligned}$
So option (1) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366427 The thickness of a metallic plate is $0.4 c m$ . The temperature between its two surface is $20^{\circ} C$ . The quantity of heat flowing per second is 50 $c a l$ from $5 c m^{2}$ area. In $C G S$ system, the coefficient of thermal conductivity will be

1 0.4

2 0.6

3 0.2

4 0.5

Explanation:

$\frac{Q}{t} = \frac{K A (Δ θ)}{l} \Rightarrow 50 = \frac{5 \times 20 K}{0.4}$
$\Rightarrow K = \frac{1}{5} = 0.2$