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Six identical metallic rods are joined together in a pattern as shown in the figure. Points A and D are maintained at temperatures ${60}^o$C and ${240}^{\mathrm{o}}$C. The temperature of the junction B will be :

1. ${120}^{\mathrm{o}}$C
2. ${150}^{\mathrm{o}}$C
3. ${60}^{\mathrm{o}}$C
4. ${80}^{\mathrm{o}}$C

Two rods A and B are of equal lengths. Their ends are kept between the same temperatures and their area of cross-sections are ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ and thermal conductivities are ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$. The rate of heat transmission in the two rods will be equal, if :
1. ${\mathrm{K}}_1{\mathrm{A}}_2<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{K}}_2{\mathrm{A}}_1$
2. ${\mathrm{K}}_1{\mathrm{A}}_1<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{K}}_2{\mathrm{A}}_2$
3. ${\mathrm{K}}_1<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{K}}_2$
4. ${\mathrm{K}}_1{\mathrm{A}}_1^2<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{K}}_2{\mathrm{A}}_2^2$

Two rods of the same length and the same material transfer a given amount of heat in 12 seconds when they are joined end to end. But when they are joined lengthwise, then they will transfer the same heat in the same conditions in :
1. 24 s
2. 3 s
3. 1.5 s
4. 48 s

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q :
1. $\frac{\mathrm{Q}}{<mspace\; width="1em"></mspace>4{\mathrm{\pi R}}^2\mathrm{\sigma }}$
2. ${\left(\frac{\mathrm{Q}}{4{\mathrm{\pi R}}^2\mathrm{\sigma }}\right)}^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$
3. ${\left(\frac{4{\mathrm{\pi R}}^2\mathrm{Q}}{\sigma }\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$
4. ${\left(\frac{Q}{4{\mathrm{\pi R}}^2\mathrm{\sigma }}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$

The tungsten filament of an electric lamp has a surface area A and a power rating P. If the emissivity of the filament is $\mathrm{\epsilon }$ and $\mathrm{\sigma }$ is Stefan's constant, the steady temperature of the filament will be :
1. $\mathrm{T}={\left(\frac{\mathrm{P}}{\mathrm{A\epsilon \sigma }}\right)}^4$
2. $\mathrm{T}=\left(\frac{\mathrm{P}}{\mathrm{A\epsilon \sigma }}\right)$
3. $\mathrm{T}={\left(\frac{\mathrm{A\epsilon \sigma }}{P}\right)}^{1/4}$
4. $\mathrm{T}={\left(\frac{\mathrm{P}}{\mathrm{A\epsilon \sigma }}\right)}^{1/4}$

Assuming the sun to have a spherical outer surface of radius r radiating like a black body at temperature $\mathrm{t}°\mathrm{C}$, the power received by a unit surface, (normal the incident rays) at a distance R from the centre of the sun is :
1. $\frac{4{\mathrm{\pi r}}^2{\mathrm{\sigma t}}^4}{{\mathrm{R}}^2}$
2. $\frac{{\mathrm{r}}^2\mathrm{\sigma }{\left(\mathrm{t}+273\right)}^4}{4{\mathrm{\pi R}}^2}$
3. $\frac{16{\mathrm{\pi }}^2{\mathrm{r}}^2{\mathrm{\sigma t}}^4}{{\mathrm{R}}^2}$
4. $\frac{{\mathrm{r}}^2\mathrm{\sigma }{\left(\mathrm{t}+273\right)}^4}{{\mathrm{R}}^2}$

Two spherical black bodies of radii ${\mathrm{r}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{r}}_2$ and with surface temperature ${\mathrm{T}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{T}}_2$ respectively radiate the same power. Then the ratio of ${\mathrm{r}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{r}}_2$ will be :
1. ${\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)}^2$
2. ${\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)}^4$
3. ${\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^2$
4. ${\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^4$

Two rods (one semi-circular and other straight) of the same material and of the same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperatures. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross-section of straight rod in a given time is :

1. $2:\mathrm{\pi }$
2. 1:2
3. $\mathrm{\pi }:2$
4. 3:2

The temperatures of the outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thicknesses x and 4x, respectively are ${\mathrm{T}}_2<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{T}}_1<mspace\; width="1em"></mspace>\left({\mathrm{T}}_2>{\mathrm{T}}_1\right)$. The rate of heat transfer through the slab, in a steady-state, is $\left(\frac{\mathrm{A}\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)\mathrm{K}}{\mathrm{x}}\right)f$, with f is equal to :

1. 1
2. 1/2
3. 2/3
4. 1/3

A composite metal bar of the uniform section is made up of length 25 cm of copper, 10 cm of nickel and 15 cm of aluminium. Each part is in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at 100$°$C and the aluminium end at 0$°$C. The whole rod is covered with a belt so that no heat loss occurs at the sides. If ${\mathrm{K}}_{\mathrm{Cu}}=2{\mathrm{K}}_{\mathrm{Al}}$ and ${\mathrm{K}}_{\mathrm{Al}}=3{\mathrm{K}}_{\mathrm{Ni}}$, then what will be the temperatures of Cu-Ni and Ni-Al junctions respectively?

1. 23.33$°$C and 78.8$°$C
2. 83.33$°$C and 20$°$C
3. 50$°$C and 30$°$C
4. 30$°$C and 50$°$C

Five rods of the same dimensions are arranged as shown in the figure. They have thermal conductivities ${\mathrm{K}}_1,<mspace\; width="1em"></mspace>{\mathrm{K}}_2,<mspace\; width="1em"></mspace>{\mathrm{K}}_3,<mspace\; width="1em"></mspace>{\mathrm{K}}_4<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{K}}_5$. When points A and B are maintained at different temperatures, no heat flows through the central rod if :

1. ${\mathrm{K}}_1={\mathrm{K}}_4<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{K}}_2={\mathrm{K}}_3$
2. ${\mathrm{K}}_1{\mathrm{K}}_4={\mathrm{K}}_2{\mathrm{K}}_3$
3. ${\mathrm{K}}_1{\mathrm{K}}_2={\mathrm{K}}_3{\mathrm{K}}_4$
4. $\frac{{\mathrm{K}}_1}{{\mathrm{K}}_4}=\frac{K_2}{K_3}$

Two rectangular blocks, having identical dimensions, can be arranged either in the configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity k and the other has 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is : 

1. 2.0 s
2. 3.0 s
3. 4.5 s
4. 6.0 s

A body initially at 80$°$C cools to 64$°$C in 5 minutes and to 52$°$C in 10 minutes. The temperature of the body after 15 minutes will be :
1. 42.7$°$C
2. 35$°$C
3. 47$°$C
4. 40$°$C

Shown below the black body radiation curves at temperatures ${\mathrm{T}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{T}}_2<mspace\; width="1em"></mspace>\left({\mathrm{T}}_2>{\mathrm{T}}_1\right)$. Which of the following plots is correct?
1. 
2. 
3. 
4. 

Heat is produced at a rate given by H in a resistor when it is connected across a supply voltage V. If now the resistance of the resistor is doubled and the supply voltage is made V/3, then the rate production of heat in the resistor will be :
1. $\frac{\mathrm{H}}{18}$
2. $\frac{\mathrm{H}}{9}$
3. 6 H
4. 18 H