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PHXI11:THERMAL PROPERTIES OF MATTER

366819 Assertion :
Water expands both when heated or cooled from $4^{\circ} C$ .
Reason :
Density of water is minimum at $4^{\circ} C$ .

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:

At $4^{\circ} C$ the volume of water is minimum. When it is cooled below $4^{\circ} C$ or heated above $4^{\circ} C$ , then its volume increases. As volume at $4^{\circ} C$ is minimum, thus its density will be maximum. So option (3) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366820 A solid body of linear expansion coefficient $2 \times 10^{- 5} {(^{\circ} C)}^{- 1}$ floats in a liquid with $20 %$ of its volume out of the liquid at a temperature $20^{\circ} C$ . The volumetric expansion coefficient of liquid is 3 times that of the solid body's volumetric expansion coefficient. If the temperature is increased to $70^{\circ} C$ , the new dfraction of the body's volume out of the liquid will be approximately;

1

19.7 %

2

20.1 %

3

19.5 %

4

20.7 %

Explanation:

Let $V_{S}$ is the volume submerged, $V_{T}$ is the total volume of the solid
$\frac{V_{S}}{V_{T}} = \frac{ρ_{b}}{ρ_{L}} = 0.8$
$ρ_{b} -$ density of block; $ρ_{L} -$ density of liquid
$\begin{aligned} Δ T & = 50^{\circ} C \\ \frac{V_{S}^{'}}{V_{T}^{'}} & = \frac{ρ_{b}^{'}}{ρ_{L}^{'}} = \frac{ρ_{b}}{ρ_{L}} \times \frac{1 + γ_{L} Δ T}{1 + γ_{b} Δ T} \\ = 0.8 \times (\frac{1 + 18 \times 10^{- 5} \times 50}{1 + 6 \times 10^{- 5} \times 50}) \\ = 0.8 \times (\frac{1 + 9 \times 10^{- 3}}{1 + 3 \times 10^{- 3}}) \\ = 0.8 \times (1 + 6 \times 10^{- 3}) \\ \frac{V_{T}^{'} - V_{S}^{'}}{V_{T}^{'}} & = 1 - 0.8 - 0.8 \times 6 \times 10^{- 3} \\ = & 0.1952 \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366821 The coefficient of volume expansion of glycerine is $49 \times 10^{- 5} / K$ . What is the fractional change in its density for a $30^{\circ} C$ rise in temperature?

1

1.45 \times 10^{- 3}

2

2.45 \times 10^{- 3}

3

2.45 \times 10^{- 2}

4

1.45 \times 10^{- 2}

Explanation:

Given, coefficient of volume expension
$(γ) = 49 \times 10^{- 5} / K$
Rise in temperature $(Δ T) = 30^{\circ} C$
Let initial volume of glycerine be $V_{0}$ .
Volume of glycerine when temperature is increased by $30^{\circ} C$
$V = V_{0} [1 + γ Δ T]$
$= V_{0} [1 + 49 \times 10^{- 5} \times 30]$
$= V_{0} [1 + 0.01470] = 1.0147 V_{0}$
$\frac{V_{0}}{V} = \frac{1}{1.0147} (1)$
$\frac{ρ}{ρ_{0}} = \frac{m / V}{m / V_{0}} = \frac{V_{0}}{V} = \frac{1}{1.0147} (2)$
Fractional change in density
$= \frac{Δ ρ}{ρ_{0}} = \frac{ρ - ρ_{0}}{ρ_{0}} = \frac{ρ}{ρ_{0}} - 1$
Substituting value from Eq. (2), we get
Fractional change in density $= \frac{1}{1.0147} - 1$
$= - 1.45 \times 10^{- 2}$
Negative sign shows that the density of glycerine decrease with rise in temperature

NCERT Exempler

PHXI11:THERMAL PROPERTIES OF MATTER

366822 Why does a glass beaker sometimes break, if we quickly pour boiling water into it?

1 Hot water expands, pushing the glass out

2 The hot water cools when it touches the glass, shrinking and pulling the glass in

3 The glass becomes hot and expands causing the molecules to break

4 The inside of the glass expands faster than the outside of the glass, causing the glass to break

PHXI11:THERMAL PROPERTIES OF MATTER

366823 Water has maximum density at

1

0^{\circ} C

2

4^{\circ} C

3

25^{\circ} C

4

37^{\circ} C

PHXI11:THERMAL PROPERTIES OF MATTER

366819 Assertion :
Water expands both when heated or cooled from $4^{\circ} C$ .
Reason :
Density of water is minimum at $4^{\circ} C$ .

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:

At $4^{\circ} C$ the volume of water is minimum. When it is cooled below $4^{\circ} C$ or heated above $4^{\circ} C$ , then its volume increases. As volume at $4^{\circ} C$ is minimum, thus its density will be maximum. So option (3) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366820 A solid body of linear expansion coefficient $2 \times 10^{- 5} {(^{\circ} C)}^{- 1}$ floats in a liquid with $20 %$ of its volume out of the liquid at a temperature $20^{\circ} C$ . The volumetric expansion coefficient of liquid is 3 times that of the solid body's volumetric expansion coefficient. If the temperature is increased to $70^{\circ} C$ , the new dfraction of the body's volume out of the liquid will be approximately;

1

19.7 %

2

20.1 %

3

19.5 %

4

20.7 %

Explanation:

Let $V_{S}$ is the volume submerged, $V_{T}$ is the total volume of the solid
$\frac{V_{S}}{V_{T}} = \frac{ρ_{b}}{ρ_{L}} = 0.8$
$ρ_{b} -$ density of block; $ρ_{L} -$ density of liquid
$\begin{aligned} Δ T & = 50^{\circ} C \\ \frac{V_{S}^{'}}{V_{T}^{'}} & = \frac{ρ_{b}^{'}}{ρ_{L}^{'}} = \frac{ρ_{b}}{ρ_{L}} \times \frac{1 + γ_{L} Δ T}{1 + γ_{b} Δ T} \\ = 0.8 \times (\frac{1 + 18 \times 10^{- 5} \times 50}{1 + 6 \times 10^{- 5} \times 50}) \\ = 0.8 \times (\frac{1 + 9 \times 10^{- 3}}{1 + 3 \times 10^{- 3}}) \\ = 0.8 \times (1 + 6 \times 10^{- 3}) \\ \frac{V_{T}^{'} - V_{S}^{'}}{V_{T}^{'}} & = 1 - 0.8 - 0.8 \times 6 \times 10^{- 3} \\ = & 0.1952 \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366821 The coefficient of volume expansion of glycerine is $49 \times 10^{- 5} / K$ . What is the fractional change in its density for a $30^{\circ} C$ rise in temperature?

1

1.45 \times 10^{- 3}

2

2.45 \times 10^{- 3}

3

2.45 \times 10^{- 2}

4

1.45 \times 10^{- 2}

Explanation:

Given, coefficient of volume expension
$(γ) = 49 \times 10^{- 5} / K$
Rise in temperature $(Δ T) = 30^{\circ} C$
Let initial volume of glycerine be $V_{0}$ .
Volume of glycerine when temperature is increased by $30^{\circ} C$
$V = V_{0} [1 + γ Δ T]$
$= V_{0} [1 + 49 \times 10^{- 5} \times 30]$
$= V_{0} [1 + 0.01470] = 1.0147 V_{0}$
$\frac{V_{0}}{V} = \frac{1}{1.0147} (1)$
$\frac{ρ}{ρ_{0}} = \frac{m / V}{m / V_{0}} = \frac{V_{0}}{V} = \frac{1}{1.0147} (2)$
Fractional change in density
$= \frac{Δ ρ}{ρ_{0}} = \frac{ρ - ρ_{0}}{ρ_{0}} = \frac{ρ}{ρ_{0}} - 1$
Substituting value from Eq. (2), we get
Fractional change in density $= \frac{1}{1.0147} - 1$
$= - 1.45 \times 10^{- 2}$
Negative sign shows that the density of glycerine decrease with rise in temperature

NCERT Exempler

PHXI11:THERMAL PROPERTIES OF MATTER

366822 Why does a glass beaker sometimes break, if we quickly pour boiling water into it?

1 Hot water expands, pushing the glass out

2 The hot water cools when it touches the glass, shrinking and pulling the glass in

3 The glass becomes hot and expands causing the molecules to break

4 The inside of the glass expands faster than the outside of the glass, causing the glass to break

PHXI11:THERMAL PROPERTIES OF MATTER

366823 Water has maximum density at

1

0^{\circ} C

2

4^{\circ} C

3

25^{\circ} C

4

37^{\circ} C

PHXI11:THERMAL PROPERTIES OF MATTER

366819 Assertion :
Water expands both when heated or cooled from $4^{\circ} C$ .
Reason :
Density of water is minimum at $4^{\circ} C$ .

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:

At $4^{\circ} C$ the volume of water is minimum. When it is cooled below $4^{\circ} C$ or heated above $4^{\circ} C$ , then its volume increases. As volume at $4^{\circ} C$ is minimum, thus its density will be maximum. So option (3) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366820 A solid body of linear expansion coefficient $2 \times 10^{- 5} {(^{\circ} C)}^{- 1}$ floats in a liquid with $20 %$ of its volume out of the liquid at a temperature $20^{\circ} C$ . The volumetric expansion coefficient of liquid is 3 times that of the solid body's volumetric expansion coefficient. If the temperature is increased to $70^{\circ} C$ , the new dfraction of the body's volume out of the liquid will be approximately;

1

19.7 %

2

20.1 %

3

19.5 %

4

20.7 %

Explanation:

Let $V_{S}$ is the volume submerged, $V_{T}$ is the total volume of the solid
$\frac{V_{S}}{V_{T}} = \frac{ρ_{b}}{ρ_{L}} = 0.8$
$ρ_{b} -$ density of block; $ρ_{L} -$ density of liquid
$\begin{aligned} Δ T & = 50^{\circ} C \\ \frac{V_{S}^{'}}{V_{T}^{'}} & = \frac{ρ_{b}^{'}}{ρ_{L}^{'}} = \frac{ρ_{b}}{ρ_{L}} \times \frac{1 + γ_{L} Δ T}{1 + γ_{b} Δ T} \\ = 0.8 \times (\frac{1 + 18 \times 10^{- 5} \times 50}{1 + 6 \times 10^{- 5} \times 50}) \\ = 0.8 \times (\frac{1 + 9 \times 10^{- 3}}{1 + 3 \times 10^{- 3}}) \\ = 0.8 \times (1 + 6 \times 10^{- 3}) \\ \frac{V_{T}^{'} - V_{S}^{'}}{V_{T}^{'}} & = 1 - 0.8 - 0.8 \times 6 \times 10^{- 3} \\ = & 0.1952 \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366821 The coefficient of volume expansion of glycerine is $49 \times 10^{- 5} / K$ . What is the fractional change in its density for a $30^{\circ} C$ rise in temperature?

1

1.45 \times 10^{- 3}

2

2.45 \times 10^{- 3}

3

2.45 \times 10^{- 2}

4

1.45 \times 10^{- 2}

Explanation:

Given, coefficient of volume expension
$(γ) = 49 \times 10^{- 5} / K$
Rise in temperature $(Δ T) = 30^{\circ} C$
Let initial volume of glycerine be $V_{0}$ .
Volume of glycerine when temperature is increased by $30^{\circ} C$
$V = V_{0} [1 + γ Δ T]$
$= V_{0} [1 + 49 \times 10^{- 5} \times 30]$
$= V_{0} [1 + 0.01470] = 1.0147 V_{0}$
$\frac{V_{0}}{V} = \frac{1}{1.0147} (1)$
$\frac{ρ}{ρ_{0}} = \frac{m / V}{m / V_{0}} = \frac{V_{0}}{V} = \frac{1}{1.0147} (2)$
Fractional change in density
$= \frac{Δ ρ}{ρ_{0}} = \frac{ρ - ρ_{0}}{ρ_{0}} = \frac{ρ}{ρ_{0}} - 1$
Substituting value from Eq. (2), we get
Fractional change in density $= \frac{1}{1.0147} - 1$
$= - 1.45 \times 10^{- 2}$
Negative sign shows that the density of glycerine decrease with rise in temperature

NCERT Exempler

PHXI11:THERMAL PROPERTIES OF MATTER

366822 Why does a glass beaker sometimes break, if we quickly pour boiling water into it?

1 Hot water expands, pushing the glass out

2 The hot water cools when it touches the glass, shrinking and pulling the glass in

3 The glass becomes hot and expands causing the molecules to break

4 The inside of the glass expands faster than the outside of the glass, causing the glass to break

PHXI11:THERMAL PROPERTIES OF MATTER

366823 Water has maximum density at

1

0^{\circ} C

2

4^{\circ} C

3

25^{\circ} C

4

37^{\circ} C

PHXI11:THERMAL PROPERTIES OF MATTER

366819 Assertion :
Water expands both when heated or cooled from $4^{\circ} C$ .
Reason :
Density of water is minimum at $4^{\circ} C$ .

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:

At $4^{\circ} C$ the volume of water is minimum. When it is cooled below $4^{\circ} C$ or heated above $4^{\circ} C$ , then its volume increases. As volume at $4^{\circ} C$ is minimum, thus its density will be maximum. So option (3) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366820 A solid body of linear expansion coefficient $2 \times 10^{- 5} {(^{\circ} C)}^{- 1}$ floats in a liquid with $20 %$ of its volume out of the liquid at a temperature $20^{\circ} C$ . The volumetric expansion coefficient of liquid is 3 times that of the solid body's volumetric expansion coefficient. If the temperature is increased to $70^{\circ} C$ , the new dfraction of the body's volume out of the liquid will be approximately;

1

19.7 %

2

20.1 %

3

19.5 %

4

20.7 %

Explanation:

Let $V_{S}$ is the volume submerged, $V_{T}$ is the total volume of the solid
$\frac{V_{S}}{V_{T}} = \frac{ρ_{b}}{ρ_{L}} = 0.8$
$ρ_{b} -$ density of block; $ρ_{L} -$ density of liquid
$\begin{aligned} Δ T & = 50^{\circ} C \\ \frac{V_{S}^{'}}{V_{T}^{'}} & = \frac{ρ_{b}^{'}}{ρ_{L}^{'}} = \frac{ρ_{b}}{ρ_{L}} \times \frac{1 + γ_{L} Δ T}{1 + γ_{b} Δ T} \\ = 0.8 \times (\frac{1 + 18 \times 10^{- 5} \times 50}{1 + 6 \times 10^{- 5} \times 50}) \\ = 0.8 \times (\frac{1 + 9 \times 10^{- 3}}{1 + 3 \times 10^{- 3}}) \\ = 0.8 \times (1 + 6 \times 10^{- 3}) \\ \frac{V_{T}^{'} - V_{S}^{'}}{V_{T}^{'}} & = 1 - 0.8 - 0.8 \times 6 \times 10^{- 3} \\ = & 0.1952 \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366821 The coefficient of volume expansion of glycerine is $49 \times 10^{- 5} / K$ . What is the fractional change in its density for a $30^{\circ} C$ rise in temperature?

1

1.45 \times 10^{- 3}

2

2.45 \times 10^{- 3}

3

2.45 \times 10^{- 2}

4

1.45 \times 10^{- 2}

Explanation:

Given, coefficient of volume expension
$(γ) = 49 \times 10^{- 5} / K$
Rise in temperature $(Δ T) = 30^{\circ} C$
Let initial volume of glycerine be $V_{0}$ .
Volume of glycerine when temperature is increased by $30^{\circ} C$
$V = V_{0} [1 + γ Δ T]$
$= V_{0} [1 + 49 \times 10^{- 5} \times 30]$
$= V_{0} [1 + 0.01470] = 1.0147 V_{0}$
$\frac{V_{0}}{V} = \frac{1}{1.0147} (1)$
$\frac{ρ}{ρ_{0}} = \frac{m / V}{m / V_{0}} = \frac{V_{0}}{V} = \frac{1}{1.0147} (2)$
Fractional change in density
$= \frac{Δ ρ}{ρ_{0}} = \frac{ρ - ρ_{0}}{ρ_{0}} = \frac{ρ}{ρ_{0}} - 1$
Substituting value from Eq. (2), we get
Fractional change in density $= \frac{1}{1.0147} - 1$
$= - 1.45 \times 10^{- 2}$
Negative sign shows that the density of glycerine decrease with rise in temperature

NCERT Exempler

PHXI11:THERMAL PROPERTIES OF MATTER

366822 Why does a glass beaker sometimes break, if we quickly pour boiling water into it?

1 Hot water expands, pushing the glass out

2 The hot water cools when it touches the glass, shrinking and pulling the glass in

3 The glass becomes hot and expands causing the molecules to break

4 The inside of the glass expands faster than the outside of the glass, causing the glass to break

PHXI11:THERMAL PROPERTIES OF MATTER

366823 Water has maximum density at

1

0^{\circ} C

2

4^{\circ} C

3

25^{\circ} C

4

37^{\circ} C

PHXI11:THERMAL PROPERTIES OF MATTER

366819 Assertion :
Water expands both when heated or cooled from $4^{\circ} C$ .
Reason :
Density of water is minimum at $4^{\circ} C$ .

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:

At $4^{\circ} C$ the volume of water is minimum. When it is cooled below $4^{\circ} C$ or heated above $4^{\circ} C$ , then its volume increases. As volume at $4^{\circ} C$ is minimum, thus its density will be maximum. So option (3) is correct.

PHXI11:THERMAL PROPERTIES OF MATTER

366820 A solid body of linear expansion coefficient $2 \times 10^{- 5} {(^{\circ} C)}^{- 1}$ floats in a liquid with $20 %$ of its volume out of the liquid at a temperature $20^{\circ} C$ . The volumetric expansion coefficient of liquid is 3 times that of the solid body's volumetric expansion coefficient. If the temperature is increased to $70^{\circ} C$ , the new dfraction of the body's volume out of the liquid will be approximately;

1

19.7 %

2

20.1 %

3

19.5 %

4

20.7 %

Explanation:

Let $V_{S}$ is the volume submerged, $V_{T}$ is the total volume of the solid
$\frac{V_{S}}{V_{T}} = \frac{ρ_{b}}{ρ_{L}} = 0.8$
$ρ_{b} -$ density of block; $ρ_{L} -$ density of liquid
$\begin{aligned} Δ T & = 50^{\circ} C \\ \frac{V_{S}^{'}}{V_{T}^{'}} & = \frac{ρ_{b}^{'}}{ρ_{L}^{'}} = \frac{ρ_{b}}{ρ_{L}} \times \frac{1 + γ_{L} Δ T}{1 + γ_{b} Δ T} \\ = 0.8 \times (\frac{1 + 18 \times 10^{- 5} \times 50}{1 + 6 \times 10^{- 5} \times 50}) \\ = 0.8 \times (\frac{1 + 9 \times 10^{- 3}}{1 + 3 \times 10^{- 3}}) \\ = 0.8 \times (1 + 6 \times 10^{- 3}) \\ \frac{V_{T}^{'} - V_{S}^{'}}{V_{T}^{'}} & = 1 - 0.8 - 0.8 \times 6 \times 10^{- 3} \\ = & 0.1952 \end{aligned}$

PHXI11:THERMAL PROPERTIES OF MATTER

366821 The coefficient of volume expansion of glycerine is $49 \times 10^{- 5} / K$ . What is the fractional change in its density for a $30^{\circ} C$ rise in temperature?

1

1.45 \times 10^{- 3}

2

2.45 \times 10^{- 3}

3

2.45 \times 10^{- 2}

4

1.45 \times 10^{- 2}

Explanation:

Given, coefficient of volume expension
$(γ) = 49 \times 10^{- 5} / K$
Rise in temperature $(Δ T) = 30^{\circ} C$
Let initial volume of glycerine be $V_{0}$ .
Volume of glycerine when temperature is increased by $30^{\circ} C$
$V = V_{0} [1 + γ Δ T]$
$= V_{0} [1 + 49 \times 10^{- 5} \times 30]$
$= V_{0} [1 + 0.01470] = 1.0147 V_{0}$
$\frac{V_{0}}{V} = \frac{1}{1.0147} (1)$
$\frac{ρ}{ρ_{0}} = \frac{m / V}{m / V_{0}} = \frac{V_{0}}{V} = \frac{1}{1.0147} (2)$
Fractional change in density
$= \frac{Δ ρ}{ρ_{0}} = \frac{ρ - ρ_{0}}{ρ_{0}} = \frac{ρ}{ρ_{0}} - 1$
Substituting value from Eq. (2), we get
Fractional change in density $= \frac{1}{1.0147} - 1$
$= - 1.45 \times 10^{- 2}$
Negative sign shows that the density of glycerine decrease with rise in temperature

NCERT Exempler

PHXI11:THERMAL PROPERTIES OF MATTER

366822 Why does a glass beaker sometimes break, if we quickly pour boiling water into it?

1 Hot water expands, pushing the glass out

2 The hot water cools when it touches the glass, shrinking and pulling the glass in

3 The glass becomes hot and expands causing the molecules to break

4 The inside of the glass expands faster than the outside of the glass, causing the glass to break

PHXI11:THERMAL PROPERTIES OF MATTER

366823 Water has maximum density at

1

0^{\circ} C

2

4^{\circ} C

3

25^{\circ} C

4

37^{\circ} C