01. Thermal Expansion (Linear, Area and Volume Expansion)
Thermal Properties of Matter

146533 A piece of metal weighs $45 \mathrm{~g}$ in air and $25 \mathrm{~g}$ in a liquid of density $1.5 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3} \mathrm{kept}$ at $30^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $40^{\circ} \mathrm{C}$, the metal piece weights $27 \mathrm{~g}$. The density of liquid of $40^{\circ} \mathrm{C}$ is $1.25 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3}$, the coefficient of linear expansion of metal is

1 $1.3 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
2 $5.2 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
3 $2.6 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
4 $0.26 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
Thermal Properties of Matter

146534 A metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{0} C$. What is the force required to prevent the expansion of the rod lengthwise ?
( $Y$ = Young's modulus of material of the rod, $\alpha$ = coefficient of linear expansion of the rod).

1 $\mathrm{YA} \alpha \mathrm{T} /(1-\alpha \mathrm{T})$
2 $\mathrm{YA} \alpha \mathrm{T} /(1+\alpha \mathrm{T})$
3 $\mathrm{YA} \alpha / \mathrm{T}(1+\alpha \mathrm{T})$
4 $\mathrm{YA} \alpha /(1-\alpha \mathrm{T})$
Thermal Properties of Matter

146535 A hole is drilled in a copper sheet. The diameter of the hole is $4.24 \mathrm{~cm}$ at $27.0^{\circ} \mathrm{C}$. What is the change in the diameter of the hole when the sheet is heated to $227^{\circ} \mathrm{C}$ ? Coefficient of linear expansion of copper $=1.70 \times 10^{-5} \mathrm{~K}^{-1}$

1 $0.0144 \mathrm{~cm}$
2 $0.144 \mathrm{~cm}$
3 $1.44 \mathrm{~cm}$
4 $0.0014 \mathrm{~cm}$
Thermal Properties of Matter

146536 A brass rod of length $50 \mathrm{~cm}$ and diameter 3.0 $\mathrm{mm}$ is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250^{\circ} \mathrm{C}$, if the original lengths are at $40.0^{\circ} \mathrm{C}$ ? (coefficient of linear expansion of brass $=2.0 \times 10^{-5} \mathrm{~K}^{-1}$, steel $=$ $1.2 \times 10^{-5} \mathrm{~K}^{-1}$ )

1 $0.4365 \mathrm{~cm}$
2 $0.5525 \mathrm{~cm}$
3 $0.3465 \mathrm{~cm}$
4 $0.2465 \mathrm{~cm}$
Thermal Properties of Matter

146537 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. What is the fractional change in its density for $\mathrm{ar}^{\circ} \mathrm{C}$ rise in temperature?

1 0.0145
2 0.0154
3 0.154
4 $1.144 \mathrm{w}$
Thermal Properties of Matter

146533 A piece of metal weighs $45 \mathrm{~g}$ in air and $25 \mathrm{~g}$ in a liquid of density $1.5 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3} \mathrm{kept}$ at $30^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $40^{\circ} \mathrm{C}$, the metal piece weights $27 \mathrm{~g}$. The density of liquid of $40^{\circ} \mathrm{C}$ is $1.25 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3}$, the coefficient of linear expansion of metal is

1 $1.3 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
2 $5.2 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
3 $2.6 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
4 $0.26 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
Thermal Properties of Matter

146534 A metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{0} C$. What is the force required to prevent the expansion of the rod lengthwise ?
( $Y$ = Young's modulus of material of the rod, $\alpha$ = coefficient of linear expansion of the rod).

1 $\mathrm{YA} \alpha \mathrm{T} /(1-\alpha \mathrm{T})$
2 $\mathrm{YA} \alpha \mathrm{T} /(1+\alpha \mathrm{T})$
3 $\mathrm{YA} \alpha / \mathrm{T}(1+\alpha \mathrm{T})$
4 $\mathrm{YA} \alpha /(1-\alpha \mathrm{T})$
Thermal Properties of Matter

146535 A hole is drilled in a copper sheet. The diameter of the hole is $4.24 \mathrm{~cm}$ at $27.0^{\circ} \mathrm{C}$. What is the change in the diameter of the hole when the sheet is heated to $227^{\circ} \mathrm{C}$ ? Coefficient of linear expansion of copper $=1.70 \times 10^{-5} \mathrm{~K}^{-1}$

1 $0.0144 \mathrm{~cm}$
2 $0.144 \mathrm{~cm}$
3 $1.44 \mathrm{~cm}$
4 $0.0014 \mathrm{~cm}$
Thermal Properties of Matter

146536 A brass rod of length $50 \mathrm{~cm}$ and diameter 3.0 $\mathrm{mm}$ is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250^{\circ} \mathrm{C}$, if the original lengths are at $40.0^{\circ} \mathrm{C}$ ? (coefficient of linear expansion of brass $=2.0 \times 10^{-5} \mathrm{~K}^{-1}$, steel $=$ $1.2 \times 10^{-5} \mathrm{~K}^{-1}$ )

1 $0.4365 \mathrm{~cm}$
2 $0.5525 \mathrm{~cm}$
3 $0.3465 \mathrm{~cm}$
4 $0.2465 \mathrm{~cm}$
Thermal Properties of Matter

146537 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. What is the fractional change in its density for $\mathrm{ar}^{\circ} \mathrm{C}$ rise in temperature?

1 0.0145
2 0.0154
3 0.154
4 $1.144 \mathrm{w}$
Thermal Properties of Matter

146533 A piece of metal weighs $45 \mathrm{~g}$ in air and $25 \mathrm{~g}$ in a liquid of density $1.5 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3} \mathrm{kept}$ at $30^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $40^{\circ} \mathrm{C}$, the metal piece weights $27 \mathrm{~g}$. The density of liquid of $40^{\circ} \mathrm{C}$ is $1.25 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3}$, the coefficient of linear expansion of metal is

1 $1.3 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
2 $5.2 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
3 $2.6 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
4 $0.26 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
Thermal Properties of Matter

146534 A metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{0} C$. What is the force required to prevent the expansion of the rod lengthwise ?
( $Y$ = Young's modulus of material of the rod, $\alpha$ = coefficient of linear expansion of the rod).

1 $\mathrm{YA} \alpha \mathrm{T} /(1-\alpha \mathrm{T})$
2 $\mathrm{YA} \alpha \mathrm{T} /(1+\alpha \mathrm{T})$
3 $\mathrm{YA} \alpha / \mathrm{T}(1+\alpha \mathrm{T})$
4 $\mathrm{YA} \alpha /(1-\alpha \mathrm{T})$
Thermal Properties of Matter

146535 A hole is drilled in a copper sheet. The diameter of the hole is $4.24 \mathrm{~cm}$ at $27.0^{\circ} \mathrm{C}$. What is the change in the diameter of the hole when the sheet is heated to $227^{\circ} \mathrm{C}$ ? Coefficient of linear expansion of copper $=1.70 \times 10^{-5} \mathrm{~K}^{-1}$

1 $0.0144 \mathrm{~cm}$
2 $0.144 \mathrm{~cm}$
3 $1.44 \mathrm{~cm}$
4 $0.0014 \mathrm{~cm}$
Thermal Properties of Matter

146536 A brass rod of length $50 \mathrm{~cm}$ and diameter 3.0 $\mathrm{mm}$ is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250^{\circ} \mathrm{C}$, if the original lengths are at $40.0^{\circ} \mathrm{C}$ ? (coefficient of linear expansion of brass $=2.0 \times 10^{-5} \mathrm{~K}^{-1}$, steel $=$ $1.2 \times 10^{-5} \mathrm{~K}^{-1}$ )

1 $0.4365 \mathrm{~cm}$
2 $0.5525 \mathrm{~cm}$
3 $0.3465 \mathrm{~cm}$
4 $0.2465 \mathrm{~cm}$
Thermal Properties of Matter

146537 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. What is the fractional change in its density for $\mathrm{ar}^{\circ} \mathrm{C}$ rise in temperature?

1 0.0145
2 0.0154
3 0.154
4 $1.144 \mathrm{w}$
Thermal Properties of Matter

146533 A piece of metal weighs $45 \mathrm{~g}$ in air and $25 \mathrm{~g}$ in a liquid of density $1.5 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3} \mathrm{kept}$ at $30^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $40^{\circ} \mathrm{C}$, the metal piece weights $27 \mathrm{~g}$. The density of liquid of $40^{\circ} \mathrm{C}$ is $1.25 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3}$, the coefficient of linear expansion of metal is

1 $1.3 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
2 $5.2 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
3 $2.6 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
4 $0.26 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
Thermal Properties of Matter

146534 A metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{0} C$. What is the force required to prevent the expansion of the rod lengthwise ?
( $Y$ = Young's modulus of material of the rod, $\alpha$ = coefficient of linear expansion of the rod).

1 $\mathrm{YA} \alpha \mathrm{T} /(1-\alpha \mathrm{T})$
2 $\mathrm{YA} \alpha \mathrm{T} /(1+\alpha \mathrm{T})$
3 $\mathrm{YA} \alpha / \mathrm{T}(1+\alpha \mathrm{T})$
4 $\mathrm{YA} \alpha /(1-\alpha \mathrm{T})$
Thermal Properties of Matter

146535 A hole is drilled in a copper sheet. The diameter of the hole is $4.24 \mathrm{~cm}$ at $27.0^{\circ} \mathrm{C}$. What is the change in the diameter of the hole when the sheet is heated to $227^{\circ} \mathrm{C}$ ? Coefficient of linear expansion of copper $=1.70 \times 10^{-5} \mathrm{~K}^{-1}$

1 $0.0144 \mathrm{~cm}$
2 $0.144 \mathrm{~cm}$
3 $1.44 \mathrm{~cm}$
4 $0.0014 \mathrm{~cm}$
Thermal Properties of Matter

146536 A brass rod of length $50 \mathrm{~cm}$ and diameter 3.0 $\mathrm{mm}$ is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250^{\circ} \mathrm{C}$, if the original lengths are at $40.0^{\circ} \mathrm{C}$ ? (coefficient of linear expansion of brass $=2.0 \times 10^{-5} \mathrm{~K}^{-1}$, steel $=$ $1.2 \times 10^{-5} \mathrm{~K}^{-1}$ )

1 $0.4365 \mathrm{~cm}$
2 $0.5525 \mathrm{~cm}$
3 $0.3465 \mathrm{~cm}$
4 $0.2465 \mathrm{~cm}$
Thermal Properties of Matter

146537 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. What is the fractional change in its density for $\mathrm{ar}^{\circ} \mathrm{C}$ rise in temperature?

1 0.0145
2 0.0154
3 0.154
4 $1.144 \mathrm{w}$
Thermal Properties of Matter

146533 A piece of metal weighs $45 \mathrm{~g}$ in air and $25 \mathrm{~g}$ in a liquid of density $1.5 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3} \mathrm{kept}$ at $30^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $40^{\circ} \mathrm{C}$, the metal piece weights $27 \mathrm{~g}$. The density of liquid of $40^{\circ} \mathrm{C}$ is $1.25 \times 10^{3} \mathrm{~kg}-\mathrm{m}^{-3}$, the coefficient of linear expansion of metal is

1 $1.3 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
2 $5.2 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
3 $2.6 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
4 $0.26 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
Thermal Properties of Matter

146534 A metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{0} C$. What is the force required to prevent the expansion of the rod lengthwise ?
( $Y$ = Young's modulus of material of the rod, $\alpha$ = coefficient of linear expansion of the rod).

1 $\mathrm{YA} \alpha \mathrm{T} /(1-\alpha \mathrm{T})$
2 $\mathrm{YA} \alpha \mathrm{T} /(1+\alpha \mathrm{T})$
3 $\mathrm{YA} \alpha / \mathrm{T}(1+\alpha \mathrm{T})$
4 $\mathrm{YA} \alpha /(1-\alpha \mathrm{T})$
Thermal Properties of Matter

146535 A hole is drilled in a copper sheet. The diameter of the hole is $4.24 \mathrm{~cm}$ at $27.0^{\circ} \mathrm{C}$. What is the change in the diameter of the hole when the sheet is heated to $227^{\circ} \mathrm{C}$ ? Coefficient of linear expansion of copper $=1.70 \times 10^{-5} \mathrm{~K}^{-1}$

1 $0.0144 \mathrm{~cm}$
2 $0.144 \mathrm{~cm}$
3 $1.44 \mathrm{~cm}$
4 $0.0014 \mathrm{~cm}$
Thermal Properties of Matter

146536 A brass rod of length $50 \mathrm{~cm}$ and diameter 3.0 $\mathrm{mm}$ is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250^{\circ} \mathrm{C}$, if the original lengths are at $40.0^{\circ} \mathrm{C}$ ? (coefficient of linear expansion of brass $=2.0 \times 10^{-5} \mathrm{~K}^{-1}$, steel $=$ $1.2 \times 10^{-5} \mathrm{~K}^{-1}$ )

1 $0.4365 \mathrm{~cm}$
2 $0.5525 \mathrm{~cm}$
3 $0.3465 \mathrm{~cm}$
4 $0.2465 \mathrm{~cm}$
Thermal Properties of Matter

146537 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. What is the fractional change in its density for $\mathrm{ar}^{\circ} \mathrm{C}$ rise in temperature?

1 0.0145
2 0.0154
3 0.154
4 $1.144 \mathrm{w}$