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

146598 A copper rod of $88 \mathrm{~cm}$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is
$\left(\alpha_{\mathrm{Cu}}=1.7 \times 10^{-5} \mathrm{~K}^{-1} \text { and } \alpha_{\mathrm{Al}}=2.2 \times 10^{-5} \mathrm{~K}^{-1}\right)$

1 $113.9 \mathrm{~cm}$
2 $88 \mathrm{~cm}$
3 $68 \mathrm{~cm}$
4 $6.8 \mathrm{~cm}$
Thermal Properties of Matter

146599 A metal bar of mass $1.5 \mathrm{~kg}$ is heated at atmospheric pressure. Its temperature is increased from $30^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$. Then the work done in the process is (Volume expansion coefficient of the metal $=5 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, Density of the metal $=9 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$, Atmospheric pressure $=\mathbf{1} \times 10^{5} \mathrm{~Pa}$ )

1 $25 \times 10^{-3} \mathrm{~J}$
2 $2.5 \times 10^{-3} \mathrm{~J}$
3 $12.5 \times 10^{-3} \mathrm{~J}$
4 $1.25 \times 10^{-3} \mathrm{~J}$
Thermal Properties of Matter

146600 Two metal rods of same length and same material conduct a given amount of heat in 8 seconds, when they are joined end to end. But when they are joined in parallel, the time taken to conduct the same amount of heat under same conditions is

1 $4 \mathrm{~s}$
2 $2 \mathrm{~s}$
3 $16 \mathrm{~s}$
4 $1 \mathrm{~s}$
Thermal Properties of Matter

146601 The length of a steel rod is $5 \mathrm{~cm}$ more than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be (coefficient of linear expansion for steel and brass are $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$

1 $10 \mathrm{~cm}$
2 $20 \mathrm{~cm}$
3 $15 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Thermal Properties of Matter

146602 Two metal rods of lengths $L_{1}$ and $L_{2}$ and coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2}$ respectively are welded together to make a composite rod of length $\left(L_{1}+L_{2}\right)$ at $0^{\circ} \mathrm{C}$. Find the effective co-efficient of linear expansion of the composite rod.

1 $\frac{\mathrm{L}_{1} \alpha_{1}^{2}-\mathrm{L}_{2} \alpha_{2}^{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
2 $\frac{\mathrm{L}_{1}^{2} \alpha_{1}-\mathrm{L}_{2}^{2} \alpha_{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
3 $\frac{\mathrm{L}_{1} \mathrm{\alpha}_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}-\mathrm{L}_{2}}$
4 $\frac{\mathrm{L}_{1} \alpha_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}+\mathrm{L}_{2}}$
Thermal Properties of Matter

146598 A copper rod of $88 \mathrm{~cm}$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is
$\left(\alpha_{\mathrm{Cu}}=1.7 \times 10^{-5} \mathrm{~K}^{-1} \text { and } \alpha_{\mathrm{Al}}=2.2 \times 10^{-5} \mathrm{~K}^{-1}\right)$

1 $113.9 \mathrm{~cm}$
2 $88 \mathrm{~cm}$
3 $68 \mathrm{~cm}$
4 $6.8 \mathrm{~cm}$
Thermal Properties of Matter

146599 A metal bar of mass $1.5 \mathrm{~kg}$ is heated at atmospheric pressure. Its temperature is increased from $30^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$. Then the work done in the process is (Volume expansion coefficient of the metal $=5 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, Density of the metal $=9 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$, Atmospheric pressure $=\mathbf{1} \times 10^{5} \mathrm{~Pa}$ )

1 $25 \times 10^{-3} \mathrm{~J}$
2 $2.5 \times 10^{-3} \mathrm{~J}$
3 $12.5 \times 10^{-3} \mathrm{~J}$
4 $1.25 \times 10^{-3} \mathrm{~J}$
Thermal Properties of Matter

146600 Two metal rods of same length and same material conduct a given amount of heat in 8 seconds, when they are joined end to end. But when they are joined in parallel, the time taken to conduct the same amount of heat under same conditions is

1 $4 \mathrm{~s}$
2 $2 \mathrm{~s}$
3 $16 \mathrm{~s}$
4 $1 \mathrm{~s}$
Thermal Properties of Matter

146601 The length of a steel rod is $5 \mathrm{~cm}$ more than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be (coefficient of linear expansion for steel and brass are $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$

1 $10 \mathrm{~cm}$
2 $20 \mathrm{~cm}$
3 $15 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Thermal Properties of Matter

146602 Two metal rods of lengths $L_{1}$ and $L_{2}$ and coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2}$ respectively are welded together to make a composite rod of length $\left(L_{1}+L_{2}\right)$ at $0^{\circ} \mathrm{C}$. Find the effective co-efficient of linear expansion of the composite rod.

1 $\frac{\mathrm{L}_{1} \alpha_{1}^{2}-\mathrm{L}_{2} \alpha_{2}^{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
2 $\frac{\mathrm{L}_{1}^{2} \alpha_{1}-\mathrm{L}_{2}^{2} \alpha_{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
3 $\frac{\mathrm{L}_{1} \mathrm{\alpha}_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}-\mathrm{L}_{2}}$
4 $\frac{\mathrm{L}_{1} \alpha_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}+\mathrm{L}_{2}}$
Thermal Properties of Matter

146598 A copper rod of $88 \mathrm{~cm}$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is
$\left(\alpha_{\mathrm{Cu}}=1.7 \times 10^{-5} \mathrm{~K}^{-1} \text { and } \alpha_{\mathrm{Al}}=2.2 \times 10^{-5} \mathrm{~K}^{-1}\right)$

1 $113.9 \mathrm{~cm}$
2 $88 \mathrm{~cm}$
3 $68 \mathrm{~cm}$
4 $6.8 \mathrm{~cm}$
Thermal Properties of Matter

146599 A metal bar of mass $1.5 \mathrm{~kg}$ is heated at atmospheric pressure. Its temperature is increased from $30^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$. Then the work done in the process is (Volume expansion coefficient of the metal $=5 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, Density of the metal $=9 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$, Atmospheric pressure $=\mathbf{1} \times 10^{5} \mathrm{~Pa}$ )

1 $25 \times 10^{-3} \mathrm{~J}$
2 $2.5 \times 10^{-3} \mathrm{~J}$
3 $12.5 \times 10^{-3} \mathrm{~J}$
4 $1.25 \times 10^{-3} \mathrm{~J}$
Thermal Properties of Matter

146600 Two metal rods of same length and same material conduct a given amount of heat in 8 seconds, when they are joined end to end. But when they are joined in parallel, the time taken to conduct the same amount of heat under same conditions is

1 $4 \mathrm{~s}$
2 $2 \mathrm{~s}$
3 $16 \mathrm{~s}$
4 $1 \mathrm{~s}$
Thermal Properties of Matter

146601 The length of a steel rod is $5 \mathrm{~cm}$ more than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be (coefficient of linear expansion for steel and brass are $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$

1 $10 \mathrm{~cm}$
2 $20 \mathrm{~cm}$
3 $15 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Thermal Properties of Matter

146602 Two metal rods of lengths $L_{1}$ and $L_{2}$ and coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2}$ respectively are welded together to make a composite rod of length $\left(L_{1}+L_{2}\right)$ at $0^{\circ} \mathrm{C}$. Find the effective co-efficient of linear expansion of the composite rod.

1 $\frac{\mathrm{L}_{1} \alpha_{1}^{2}-\mathrm{L}_{2} \alpha_{2}^{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
2 $\frac{\mathrm{L}_{1}^{2} \alpha_{1}-\mathrm{L}_{2}^{2} \alpha_{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
3 $\frac{\mathrm{L}_{1} \mathrm{\alpha}_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}-\mathrm{L}_{2}}$
4 $\frac{\mathrm{L}_{1} \alpha_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}+\mathrm{L}_{2}}$
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Thermal Properties of Matter

146598 A copper rod of $88 \mathrm{~cm}$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is
$\left(\alpha_{\mathrm{Cu}}=1.7 \times 10^{-5} \mathrm{~K}^{-1} \text { and } \alpha_{\mathrm{Al}}=2.2 \times 10^{-5} \mathrm{~K}^{-1}\right)$

1 $113.9 \mathrm{~cm}$
2 $88 \mathrm{~cm}$
3 $68 \mathrm{~cm}$
4 $6.8 \mathrm{~cm}$
Thermal Properties of Matter

146599 A metal bar of mass $1.5 \mathrm{~kg}$ is heated at atmospheric pressure. Its temperature is increased from $30^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$. Then the work done in the process is (Volume expansion coefficient of the metal $=5 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, Density of the metal $=9 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$, Atmospheric pressure $=\mathbf{1} \times 10^{5} \mathrm{~Pa}$ )

1 $25 \times 10^{-3} \mathrm{~J}$
2 $2.5 \times 10^{-3} \mathrm{~J}$
3 $12.5 \times 10^{-3} \mathrm{~J}$
4 $1.25 \times 10^{-3} \mathrm{~J}$
Thermal Properties of Matter

146600 Two metal rods of same length and same material conduct a given amount of heat in 8 seconds, when they are joined end to end. But when they are joined in parallel, the time taken to conduct the same amount of heat under same conditions is

1 $4 \mathrm{~s}$
2 $2 \mathrm{~s}$
3 $16 \mathrm{~s}$
4 $1 \mathrm{~s}$
Thermal Properties of Matter

146601 The length of a steel rod is $5 \mathrm{~cm}$ more than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be (coefficient of linear expansion for steel and brass are $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$

1 $10 \mathrm{~cm}$
2 $20 \mathrm{~cm}$
3 $15 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Thermal Properties of Matter

146602 Two metal rods of lengths $L_{1}$ and $L_{2}$ and coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2}$ respectively are welded together to make a composite rod of length $\left(L_{1}+L_{2}\right)$ at $0^{\circ} \mathrm{C}$. Find the effective co-efficient of linear expansion of the composite rod.

1 $\frac{\mathrm{L}_{1} \alpha_{1}^{2}-\mathrm{L}_{2} \alpha_{2}^{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
2 $\frac{\mathrm{L}_{1}^{2} \alpha_{1}-\mathrm{L}_{2}^{2} \alpha_{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
3 $\frac{\mathrm{L}_{1} \mathrm{\alpha}_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}-\mathrm{L}_{2}}$
4 $\frac{\mathrm{L}_{1} \alpha_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}+\mathrm{L}_{2}}$
Thermal Properties of Matter

146598 A copper rod of $88 \mathrm{~cm}$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is
$\left(\alpha_{\mathrm{Cu}}=1.7 \times 10^{-5} \mathrm{~K}^{-1} \text { and } \alpha_{\mathrm{Al}}=2.2 \times 10^{-5} \mathrm{~K}^{-1}\right)$

1 $113.9 \mathrm{~cm}$
2 $88 \mathrm{~cm}$
3 $68 \mathrm{~cm}$
4 $6.8 \mathrm{~cm}$
Thermal Properties of Matter

146599 A metal bar of mass $1.5 \mathrm{~kg}$ is heated at atmospheric pressure. Its temperature is increased from $30^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$. Then the work done in the process is (Volume expansion coefficient of the metal $=5 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, Density of the metal $=9 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$, Atmospheric pressure $=\mathbf{1} \times 10^{5} \mathrm{~Pa}$ )

1 $25 \times 10^{-3} \mathrm{~J}$
2 $2.5 \times 10^{-3} \mathrm{~J}$
3 $12.5 \times 10^{-3} \mathrm{~J}$
4 $1.25 \times 10^{-3} \mathrm{~J}$
Thermal Properties of Matter

146600 Two metal rods of same length and same material conduct a given amount of heat in 8 seconds, when they are joined end to end. But when they are joined in parallel, the time taken to conduct the same amount of heat under same conditions is

1 $4 \mathrm{~s}$
2 $2 \mathrm{~s}$
3 $16 \mathrm{~s}$
4 $1 \mathrm{~s}$
Thermal Properties of Matter

146601 The length of a steel rod is $5 \mathrm{~cm}$ more than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be (coefficient of linear expansion for steel and brass are $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$

1 $10 \mathrm{~cm}$
2 $20 \mathrm{~cm}$
3 $15 \mathrm{~cm}$
4 $5 \mathrm{~cm}$
Thermal Properties of Matter

146602 Two metal rods of lengths $L_{1}$ and $L_{2}$ and coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2}$ respectively are welded together to make a composite rod of length $\left(L_{1}+L_{2}\right)$ at $0^{\circ} \mathrm{C}$. Find the effective co-efficient of linear expansion of the composite rod.

1 $\frac{\mathrm{L}_{1} \alpha_{1}^{2}-\mathrm{L}_{2} \alpha_{2}^{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
2 $\frac{\mathrm{L}_{1}^{2} \alpha_{1}-\mathrm{L}_{2}^{2} \alpha_{2}}{\mathrm{~L}_{1}^{2}+\mathrm{L}_{2}^{2}}$
3 $\frac{\mathrm{L}_{1} \mathrm{\alpha}_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}-\mathrm{L}_{2}}$
4 $\frac{\mathrm{L}_{1} \alpha_{1}+\mathrm{L}_{2} \mathrm{\alpha}_{2}}{\mathrm{~L}_{1}+\mathrm{L}_{2}}$