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

146581 Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $K_{1}$ and $K_{2}$ respectively. A steady temperature difference of $12^{\circ} \mathrm{C}$ is maintained across the composite slab. If $K_{1}=\frac{K_{2}}{2}$, the temperature difference across slab $A$ is

1 $4^{\circ} \mathrm{C}$
2 $6^{\circ} \mathrm{C}$
3 $8^{\circ} \mathrm{C}$
4 $10^{\circ} \mathrm{C}$
Thermal Properties of Matter

146582 Three rods of equal lengths are joined to form an equilateral triangle $A B C$. $D$ is the mid-point of $A B$. The coefficient of linear expansion is $\alpha_{1}$ for material of $\operatorname{rod} A B$ and $\alpha_{2}$ for material of rods $A C$ and $B C$. If the distance $D C$ remains constant for small changes in temperature, then

1 $\alpha_{1}=2 \alpha_{2}$
2 $\alpha_{1}=4 \alpha_{2}$
3 $\alpha_{1}=8 \alpha_{2}$
4 $\alpha_{1}=\alpha_{2}$
Thermal Properties of Matter

146583 A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_{C}$ and $\alpha_{B}$. On heating, the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

1 $\Delta \mathrm{T}$
2 $\frac{1}{\Delta \mathrm{T}}$
3 $\sqrt{\Delta \mathrm{T}}$
4 $\frac{1}{\sqrt{\Delta \mathrm{T}}}$
Thermal Properties of Matter

146584 On a temperature scale $Y$, water freezes at $160^{\circ} \mathrm{Y}$ and boils at $-50^{\circ} \mathrm{Y}$. On this $\mathrm{Y}$ scale, a temperature of $340 \mathrm{~K}$ is

1 $-160.3^{\circ} \mathrm{Y}$
2 $-96.3^{\circ} \mathrm{Y}$
3 $-86.3^{\circ} \mathrm{Y}$
4 $-76.3^{\circ} \mathrm{Y}$
Thermal Properties of Matter

146585 If the volume of a block of metal changes by $0.12 \%$ when heated through $20^{\circ} \mathrm{C}$, then find its coefficient of linear expansion.

1 $4 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
2 $4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
3 $2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
4 $2 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
Thermal Properties of Matter

146581 Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $K_{1}$ and $K_{2}$ respectively. A steady temperature difference of $12^{\circ} \mathrm{C}$ is maintained across the composite slab. If $K_{1}=\frac{K_{2}}{2}$, the temperature difference across slab $A$ is

1 $4^{\circ} \mathrm{C}$
2 $6^{\circ} \mathrm{C}$
3 $8^{\circ} \mathrm{C}$
4 $10^{\circ} \mathrm{C}$
Thermal Properties of Matter

146582 Three rods of equal lengths are joined to form an equilateral triangle $A B C$. $D$ is the mid-point of $A B$. The coefficient of linear expansion is $\alpha_{1}$ for material of $\operatorname{rod} A B$ and $\alpha_{2}$ for material of rods $A C$ and $B C$. If the distance $D C$ remains constant for small changes in temperature, then

1 $\alpha_{1}=2 \alpha_{2}$
2 $\alpha_{1}=4 \alpha_{2}$
3 $\alpha_{1}=8 \alpha_{2}$
4 $\alpha_{1}=\alpha_{2}$
Thermal Properties of Matter

146583 A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_{C}$ and $\alpha_{B}$. On heating, the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

1 $\Delta \mathrm{T}$
2 $\frac{1}{\Delta \mathrm{T}}$
3 $\sqrt{\Delta \mathrm{T}}$
4 $\frac{1}{\sqrt{\Delta \mathrm{T}}}$
Thermal Properties of Matter

146584 On a temperature scale $Y$, water freezes at $160^{\circ} \mathrm{Y}$ and boils at $-50^{\circ} \mathrm{Y}$. On this $\mathrm{Y}$ scale, a temperature of $340 \mathrm{~K}$ is

1 $-160.3^{\circ} \mathrm{Y}$
2 $-96.3^{\circ} \mathrm{Y}$
3 $-86.3^{\circ} \mathrm{Y}$
4 $-76.3^{\circ} \mathrm{Y}$
Thermal Properties of Matter

146585 If the volume of a block of metal changes by $0.12 \%$ when heated through $20^{\circ} \mathrm{C}$, then find its coefficient of linear expansion.

1 $4 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
2 $4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
3 $2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
4 $2 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
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Thermal Properties of Matter

146581 Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $K_{1}$ and $K_{2}$ respectively. A steady temperature difference of $12^{\circ} \mathrm{C}$ is maintained across the composite slab. If $K_{1}=\frac{K_{2}}{2}$, the temperature difference across slab $A$ is

1 $4^{\circ} \mathrm{C}$
2 $6^{\circ} \mathrm{C}$
3 $8^{\circ} \mathrm{C}$
4 $10^{\circ} \mathrm{C}$
Thermal Properties of Matter

146582 Three rods of equal lengths are joined to form an equilateral triangle $A B C$. $D$ is the mid-point of $A B$. The coefficient of linear expansion is $\alpha_{1}$ for material of $\operatorname{rod} A B$ and $\alpha_{2}$ for material of rods $A C$ and $B C$. If the distance $D C$ remains constant for small changes in temperature, then

1 $\alpha_{1}=2 \alpha_{2}$
2 $\alpha_{1}=4 \alpha_{2}$
3 $\alpha_{1}=8 \alpha_{2}$
4 $\alpha_{1}=\alpha_{2}$
Thermal Properties of Matter

146583 A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_{C}$ and $\alpha_{B}$. On heating, the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

1 $\Delta \mathrm{T}$
2 $\frac{1}{\Delta \mathrm{T}}$
3 $\sqrt{\Delta \mathrm{T}}$
4 $\frac{1}{\sqrt{\Delta \mathrm{T}}}$
Thermal Properties of Matter

146584 On a temperature scale $Y$, water freezes at $160^{\circ} \mathrm{Y}$ and boils at $-50^{\circ} \mathrm{Y}$. On this $\mathrm{Y}$ scale, a temperature of $340 \mathrm{~K}$ is

1 $-160.3^{\circ} \mathrm{Y}$
2 $-96.3^{\circ} \mathrm{Y}$
3 $-86.3^{\circ} \mathrm{Y}$
4 $-76.3^{\circ} \mathrm{Y}$
Thermal Properties of Matter

146585 If the volume of a block of metal changes by $0.12 \%$ when heated through $20^{\circ} \mathrm{C}$, then find its coefficient of linear expansion.

1 $4 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
2 $4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
3 $2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
4 $2 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
Thermal Properties of Matter

146581 Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $K_{1}$ and $K_{2}$ respectively. A steady temperature difference of $12^{\circ} \mathrm{C}$ is maintained across the composite slab. If $K_{1}=\frac{K_{2}}{2}$, the temperature difference across slab $A$ is

1 $4^{\circ} \mathrm{C}$
2 $6^{\circ} \mathrm{C}$
3 $8^{\circ} \mathrm{C}$
4 $10^{\circ} \mathrm{C}$
Thermal Properties of Matter

146582 Three rods of equal lengths are joined to form an equilateral triangle $A B C$. $D$ is the mid-point of $A B$. The coefficient of linear expansion is $\alpha_{1}$ for material of $\operatorname{rod} A B$ and $\alpha_{2}$ for material of rods $A C$ and $B C$. If the distance $D C$ remains constant for small changes in temperature, then

1 $\alpha_{1}=2 \alpha_{2}$
2 $\alpha_{1}=4 \alpha_{2}$
3 $\alpha_{1}=8 \alpha_{2}$
4 $\alpha_{1}=\alpha_{2}$
Thermal Properties of Matter

146583 A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_{C}$ and $\alpha_{B}$. On heating, the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

1 $\Delta \mathrm{T}$
2 $\frac{1}{\Delta \mathrm{T}}$
3 $\sqrt{\Delta \mathrm{T}}$
4 $\frac{1}{\sqrt{\Delta \mathrm{T}}}$
Thermal Properties of Matter

146584 On a temperature scale $Y$, water freezes at $160^{\circ} \mathrm{Y}$ and boils at $-50^{\circ} \mathrm{Y}$. On this $\mathrm{Y}$ scale, a temperature of $340 \mathrm{~K}$ is

1 $-160.3^{\circ} \mathrm{Y}$
2 $-96.3^{\circ} \mathrm{Y}$
3 $-86.3^{\circ} \mathrm{Y}$
4 $-76.3^{\circ} \mathrm{Y}$
Thermal Properties of Matter

146585 If the volume of a block of metal changes by $0.12 \%$ when heated through $20^{\circ} \mathrm{C}$, then find its coefficient of linear expansion.

1 $4 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
2 $4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
3 $2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
4 $2 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
Thermal Properties of Matter

146581 Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $K_{1}$ and $K_{2}$ respectively. A steady temperature difference of $12^{\circ} \mathrm{C}$ is maintained across the composite slab. If $K_{1}=\frac{K_{2}}{2}$, the temperature difference across slab $A$ is

1 $4^{\circ} \mathrm{C}$
2 $6^{\circ} \mathrm{C}$
3 $8^{\circ} \mathrm{C}$
4 $10^{\circ} \mathrm{C}$
Thermal Properties of Matter

146582 Three rods of equal lengths are joined to form an equilateral triangle $A B C$. $D$ is the mid-point of $A B$. The coefficient of linear expansion is $\alpha_{1}$ for material of $\operatorname{rod} A B$ and $\alpha_{2}$ for material of rods $A C$ and $B C$. If the distance $D C$ remains constant for small changes in temperature, then

1 $\alpha_{1}=2 \alpha_{2}$
2 $\alpha_{1}=4 \alpha_{2}$
3 $\alpha_{1}=8 \alpha_{2}$
4 $\alpha_{1}=\alpha_{2}$
Thermal Properties of Matter

146583 A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_{C}$ and $\alpha_{B}$. On heating, the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

1 $\Delta \mathrm{T}$
2 $\frac{1}{\Delta \mathrm{T}}$
3 $\sqrt{\Delta \mathrm{T}}$
4 $\frac{1}{\sqrt{\Delta \mathrm{T}}}$
Thermal Properties of Matter

146584 On a temperature scale $Y$, water freezes at $160^{\circ} \mathrm{Y}$ and boils at $-50^{\circ} \mathrm{Y}$. On this $\mathrm{Y}$ scale, a temperature of $340 \mathrm{~K}$ is

1 $-160.3^{\circ} \mathrm{Y}$
2 $-96.3^{\circ} \mathrm{Y}$
3 $-86.3^{\circ} \mathrm{Y}$
4 $-76.3^{\circ} \mathrm{Y}$
Thermal Properties of Matter

146585 If the volume of a block of metal changes by $0.12 \%$ when heated through $20^{\circ} \mathrm{C}$, then find its coefficient of linear expansion.

1 $4 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
2 $4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$
3 $2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$
4 $2 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$