00. Conduction
Heat Transfer

149376 The quantities of heat required to raise the temperatures of two copper spheres of radii $r_{1}$ and $r_{2}\left(r_{1}=1.5 r_{2}\right)$ through $1 \mathrm{~K}$ are in the ratio of :

1 $\frac{27}{8}$
2 $\frac{9}{4}$
3 $\frac{3}{2}$
4 1
Heat Transfer

149377 Two slabs are of the thickness $d_{1}$ and $d_{2}$. Their thermal conductivities are $K_{1}$ and $K_{2}$ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures $\theta_{1}$ and $\theta_{2}$. Assume $\theta_{1}>\theta_{2}$. The temperature $\theta$ of their common junction is

1 $\frac{\mathrm{K}_{1} \theta_{1}+\mathrm{K}_{2} \theta_{2}}{\theta_{1}+\theta_{2}}$
2 $\frac{K_{1} \theta_{1} d_{1}+K_{2} \theta_{2} d_{2}}{K_{1} d_{2}+K_{2} d_{1}}$
3 $\frac{K_{1} \theta_{1} d_{2}+K_{2} \theta_{2} d_{1}}{K_{1} d_{2}+K_{2} d_{1}}$
4 $\frac{\mathrm{K}_{1} \theta_{1}+\mathrm{K}_{2} \theta_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}$
Heat Transfer

149378 The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel ?

1 $75^{\circ} \mathrm{C}$
2 $67^{\circ} \mathrm{C}$
3 $25^{\circ} \mathrm{C}$
4 $33^{0} \mathrm{C}$
Heat Transfer

149379 Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities $k_{1}, k_{2}, k_{3}, k_{4}$ and $k_{5}$ when points $A$ and $B$ are maintained at different temperatures. No heat flows through the central rod if :

1 $\mathrm{k}_{1} \mathrm{k}_{4}=\mathrm{k}_{2} \mathrm{k}_{3}$
2 $\mathrm{k}_{1}=\mathrm{k}_{4}$ and $\mathrm{k}_{2}=\mathrm{k}_{3}$
3 $\frac{\mathrm{k}_{1}}{\mathrm{k}_{2}}=\frac{\mathrm{k}_{2}}{\mathrm{k}_{3}}$
4 $\mathrm{k}_{1} \mathrm{k}_{2}=\mathrm{k}_{3} \mathrm{k}_{4}$
Heat Transfer

149376 The quantities of heat required to raise the temperatures of two copper spheres of radii $r_{1}$ and $r_{2}\left(r_{1}=1.5 r_{2}\right)$ through $1 \mathrm{~K}$ are in the ratio of :

1 $\frac{27}{8}$
2 $\frac{9}{4}$
3 $\frac{3}{2}$
4 1
Heat Transfer

149377 Two slabs are of the thickness $d_{1}$ and $d_{2}$. Their thermal conductivities are $K_{1}$ and $K_{2}$ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures $\theta_{1}$ and $\theta_{2}$. Assume $\theta_{1}>\theta_{2}$. The temperature $\theta$ of their common junction is

1 $\frac{\mathrm{K}_{1} \theta_{1}+\mathrm{K}_{2} \theta_{2}}{\theta_{1}+\theta_{2}}$
2 $\frac{K_{1} \theta_{1} d_{1}+K_{2} \theta_{2} d_{2}}{K_{1} d_{2}+K_{2} d_{1}}$
3 $\frac{K_{1} \theta_{1} d_{2}+K_{2} \theta_{2} d_{1}}{K_{1} d_{2}+K_{2} d_{1}}$
4 $\frac{\mathrm{K}_{1} \theta_{1}+\mathrm{K}_{2} \theta_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}$
Heat Transfer

149378 The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel ?

1 $75^{\circ} \mathrm{C}$
2 $67^{\circ} \mathrm{C}$
3 $25^{\circ} \mathrm{C}$
4 $33^{0} \mathrm{C}$
Heat Transfer

149379 Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities $k_{1}, k_{2}, k_{3}, k_{4}$ and $k_{5}$ when points $A$ and $B$ are maintained at different temperatures. No heat flows through the central rod if :

1 $\mathrm{k}_{1} \mathrm{k}_{4}=\mathrm{k}_{2} \mathrm{k}_{3}$
2 $\mathrm{k}_{1}=\mathrm{k}_{4}$ and $\mathrm{k}_{2}=\mathrm{k}_{3}$
3 $\frac{\mathrm{k}_{1}}{\mathrm{k}_{2}}=\frac{\mathrm{k}_{2}}{\mathrm{k}_{3}}$
4 $\mathrm{k}_{1} \mathrm{k}_{2}=\mathrm{k}_{3} \mathrm{k}_{4}$
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Heat Transfer

149376 The quantities of heat required to raise the temperatures of two copper spheres of radii $r_{1}$ and $r_{2}\left(r_{1}=1.5 r_{2}\right)$ through $1 \mathrm{~K}$ are in the ratio of :

1 $\frac{27}{8}$
2 $\frac{9}{4}$
3 $\frac{3}{2}$
4 1
Heat Transfer

149377 Two slabs are of the thickness $d_{1}$ and $d_{2}$. Their thermal conductivities are $K_{1}$ and $K_{2}$ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures $\theta_{1}$ and $\theta_{2}$. Assume $\theta_{1}>\theta_{2}$. The temperature $\theta$ of their common junction is

1 $\frac{\mathrm{K}_{1} \theta_{1}+\mathrm{K}_{2} \theta_{2}}{\theta_{1}+\theta_{2}}$
2 $\frac{K_{1} \theta_{1} d_{1}+K_{2} \theta_{2} d_{2}}{K_{1} d_{2}+K_{2} d_{1}}$
3 $\frac{K_{1} \theta_{1} d_{2}+K_{2} \theta_{2} d_{1}}{K_{1} d_{2}+K_{2} d_{1}}$
4 $\frac{\mathrm{K}_{1} \theta_{1}+\mathrm{K}_{2} \theta_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}$
Heat Transfer

149378 The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel ?

1 $75^{\circ} \mathrm{C}$
2 $67^{\circ} \mathrm{C}$
3 $25^{\circ} \mathrm{C}$
4 $33^{0} \mathrm{C}$
Heat Transfer

149379 Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities $k_{1}, k_{2}, k_{3}, k_{4}$ and $k_{5}$ when points $A$ and $B$ are maintained at different temperatures. No heat flows through the central rod if :

1 $\mathrm{k}_{1} \mathrm{k}_{4}=\mathrm{k}_{2} \mathrm{k}_{3}$
2 $\mathrm{k}_{1}=\mathrm{k}_{4}$ and $\mathrm{k}_{2}=\mathrm{k}_{3}$
3 $\frac{\mathrm{k}_{1}}{\mathrm{k}_{2}}=\frac{\mathrm{k}_{2}}{\mathrm{k}_{3}}$
4 $\mathrm{k}_{1} \mathrm{k}_{2}=\mathrm{k}_{3} \mathrm{k}_{4}$
Heat Transfer

149376 The quantities of heat required to raise the temperatures of two copper spheres of radii $r_{1}$ and $r_{2}\left(r_{1}=1.5 r_{2}\right)$ through $1 \mathrm{~K}$ are in the ratio of :

1 $\frac{27}{8}$
2 $\frac{9}{4}$
3 $\frac{3}{2}$
4 1
Heat Transfer

149377 Two slabs are of the thickness $d_{1}$ and $d_{2}$. Their thermal conductivities are $K_{1}$ and $K_{2}$ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures $\theta_{1}$ and $\theta_{2}$. Assume $\theta_{1}>\theta_{2}$. The temperature $\theta$ of their common junction is

1 $\frac{\mathrm{K}_{1} \theta_{1}+\mathrm{K}_{2} \theta_{2}}{\theta_{1}+\theta_{2}}$
2 $\frac{K_{1} \theta_{1} d_{1}+K_{2} \theta_{2} d_{2}}{K_{1} d_{2}+K_{2} d_{1}}$
3 $\frac{K_{1} \theta_{1} d_{2}+K_{2} \theta_{2} d_{1}}{K_{1} d_{2}+K_{2} d_{1}}$
4 $\frac{\mathrm{K}_{1} \theta_{1}+\mathrm{K}_{2} \theta_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}$
Heat Transfer

149378 The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel ?

1 $75^{\circ} \mathrm{C}$
2 $67^{\circ} \mathrm{C}$
3 $25^{\circ} \mathrm{C}$
4 $33^{0} \mathrm{C}$
Heat Transfer

149379 Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities $k_{1}, k_{2}, k_{3}, k_{4}$ and $k_{5}$ when points $A$ and $B$ are maintained at different temperatures. No heat flows through the central rod if :

1 $\mathrm{k}_{1} \mathrm{k}_{4}=\mathrm{k}_{2} \mathrm{k}_{3}$
2 $\mathrm{k}_{1}=\mathrm{k}_{4}$ and $\mathrm{k}_{2}=\mathrm{k}_{3}$
3 $\frac{\mathrm{k}_{1}}{\mathrm{k}_{2}}=\frac{\mathrm{k}_{2}}{\mathrm{k}_{3}}$
4 $\mathrm{k}_{1} \mathrm{k}_{2}=\mathrm{k}_{3} \mathrm{k}_{4}$