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

146594 Consider a compound slab consisting of two different materials having equal thickneses and thermal conductivities $K$ and $2 K$, respectively. The equivalent thermal conductivity of the slab is

1 $3 \mathrm{~K}$
2 $\frac{4}{3} \mathrm{~K}$
3 $\frac{2}{3} \mathrm{~K}$
4 $\sqrt{2} \mathrm{~K}$
Thermal Properties of Matter

146595 The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_{1}$ and $T_{2}\left(T_{1}>T_{2}\right)$. The rate of heat transfer ' $\frac{\mathrm{dQ}}{\mathrm{dt}}$ ' through the rod in a steady state is given by

1 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KL}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{A}}$
2 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{K}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{LA}}$
3 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\operatorname{KLA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)$
4 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{L}}$
Thermal Properties of Matter

146596 Two rods $A$ and $B$ of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$. The thermal conductivity of the composite rod will be

1 $\frac{K_{1}+K_{2}}{2}$
2 $\frac{3\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}{2}$
3 $\mathrm{K}_{1}+\mathrm{K}_{2}$
4 $2\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)$
Thermal Properties of Matter

146597 The coefficients of linear expansions of brass and steel are $\alpha_{1}$ and $\alpha_{2}$ respectively. When we take a brass rod of length $l_{1}$ and a steel rod of length $l_{2}$ at $0^{\circ} \mathrm{C}$, then the difference in their lengths $\left(l_{2}-l_{1}\right)$ will remain the same at all temperatures, if

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

146594 Consider a compound slab consisting of two different materials having equal thickneses and thermal conductivities $K$ and $2 K$, respectively. The equivalent thermal conductivity of the slab is

1 $3 \mathrm{~K}$
2 $\frac{4}{3} \mathrm{~K}$
3 $\frac{2}{3} \mathrm{~K}$
4 $\sqrt{2} \mathrm{~K}$
Thermal Properties of Matter

146595 The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_{1}$ and $T_{2}\left(T_{1}>T_{2}\right)$. The rate of heat transfer ' $\frac{\mathrm{dQ}}{\mathrm{dt}}$ ' through the rod in a steady state is given by

1 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KL}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{A}}$
2 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{K}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{LA}}$
3 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\operatorname{KLA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)$
4 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{L}}$
Thermal Properties of Matter

146596 Two rods $A$ and $B$ of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$. The thermal conductivity of the composite rod will be

1 $\frac{K_{1}+K_{2}}{2}$
2 $\frac{3\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}{2}$
3 $\mathrm{K}_{1}+\mathrm{K}_{2}$
4 $2\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)$
Thermal Properties of Matter

146597 The coefficients of linear expansions of brass and steel are $\alpha_{1}$ and $\alpha_{2}$ respectively. When we take a brass rod of length $l_{1}$ and a steel rod of length $l_{2}$ at $0^{\circ} \mathrm{C}$, then the difference in their lengths $\left(l_{2}-l_{1}\right)$ will remain the same at all temperatures, if

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

146594 Consider a compound slab consisting of two different materials having equal thickneses and thermal conductivities $K$ and $2 K$, respectively. The equivalent thermal conductivity of the slab is

1 $3 \mathrm{~K}$
2 $\frac{4}{3} \mathrm{~K}$
3 $\frac{2}{3} \mathrm{~K}$
4 $\sqrt{2} \mathrm{~K}$
Thermal Properties of Matter

146595 The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_{1}$ and $T_{2}\left(T_{1}>T_{2}\right)$. The rate of heat transfer ' $\frac{\mathrm{dQ}}{\mathrm{dt}}$ ' through the rod in a steady state is given by

1 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KL}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{A}}$
2 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{K}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{LA}}$
3 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\operatorname{KLA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)$
4 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{L}}$
Thermal Properties of Matter

146596 Two rods $A$ and $B$ of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$. The thermal conductivity of the composite rod will be

1 $\frac{K_{1}+K_{2}}{2}$
2 $\frac{3\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}{2}$
3 $\mathrm{K}_{1}+\mathrm{K}_{2}$
4 $2\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)$
Thermal Properties of Matter

146597 The coefficients of linear expansions of brass and steel are $\alpha_{1}$ and $\alpha_{2}$ respectively. When we take a brass rod of length $l_{1}$ and a steel rod of length $l_{2}$ at $0^{\circ} \mathrm{C}$, then the difference in their lengths $\left(l_{2}-l_{1}\right)$ will remain the same at all temperatures, if

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

146594 Consider a compound slab consisting of two different materials having equal thickneses and thermal conductivities $K$ and $2 K$, respectively. The equivalent thermal conductivity of the slab is

1 $3 \mathrm{~K}$
2 $\frac{4}{3} \mathrm{~K}$
3 $\frac{2}{3} \mathrm{~K}$
4 $\sqrt{2} \mathrm{~K}$
Thermal Properties of Matter

146595 The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_{1}$ and $T_{2}\left(T_{1}>T_{2}\right)$. The rate of heat transfer ' $\frac{\mathrm{dQ}}{\mathrm{dt}}$ ' through the rod in a steady state is given by

1 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KL}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{A}}$
2 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{K}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{LA}}$
3 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\operatorname{KLA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)$
4 $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)}{\mathrm{L}}$
Thermal Properties of Matter

146596 Two rods $A$ and $B$ of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$. The thermal conductivity of the composite rod will be

1 $\frac{K_{1}+K_{2}}{2}$
2 $\frac{3\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}{2}$
3 $\mathrm{K}_{1}+\mathrm{K}_{2}$
4 $2\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)$
Thermal Properties of Matter

146597 The coefficients of linear expansions of brass and steel are $\alpha_{1}$ and $\alpha_{2}$ respectively. When we take a brass rod of length $l_{1}$ and a steel rod of length $l_{2}$ at $0^{\circ} \mathrm{C}$, then the difference in their lengths $\left(l_{2}-l_{1}\right)$ will remain the same at all temperatures, if

1 $\alpha_{1} l_{1}=\alpha_{2} l_{2}$
2 $\alpha_{1} l_{2}=\alpha_{2} l_{1}$
3 $\alpha_{1}^{2} l_{2}=\alpha_{2}^{2} l_{1}$
4 $\alpha_{1} l_{2}^{2}=\alpha_{2} l_{1}^{2}$