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

(1) 2 : $\mathrm{\pi }$ 

(2) 1 : 2

(3) $\mathrm{\pi }$ : 2

(4) 3 : 2

A wall is made up of two layers A and B. The thickness of the two layers is the same, but materials are different. The thermal conductivity of A is double than that of B. In thermal equilibrium the temperature difference between the two ends is 36$°\mathrm{C}$. Then the difference of temperature at the two surfaces of A will be

(a) 6$°\mathrm{C}$             (b) 12$°\mathrm{C}$
(c) 18$°\mathrm{C}$            (d) 24$°\mathrm{C}$

Ice starts forming in lake with water at 0$°\mathrm{C}$ and when the atmospheric temperature is -10$°\mathrm{C}$. If the time taken for 1 cm of ice be 7 hours, then the time taken for the thickness of ice to change from 1 cm to 2 cm is

(1) 7 hours                                   

(2) 14 hours

(3) Less than 7 hours                     

(4) More than 7 hours

A cylinder of radius R made of a material of thermal conductivity ${\mathrm{K}}_1$ is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of material of thermal conductivity ${\mathrm{K}}_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is 

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0$°\mathrm{C}$ and  90$°\mathrm{C}$ respectively. The temperature of the junction of the three rods will be 

(1) 45$°\mathrm{C}$

(2) 60$°\mathrm{C}$

(3) 30$°\mathrm{C}$

(4) 20$°\mathrm{C}$

A room is maintained at 20$°\mathrm{C}$ by a heater of resistance 20 ohm connected to 200 volt mains. The temperature is uniform through out the room and heat is transmitted through a glass window of area $1{\mathrm{m}}^2$ and thickness 0.2 cm. What will be the temperature outside? Given that thermal conductivity K for glass is 0.2 cal/m $°\mathrm{C}$ and J = 4.2 J/cal

(a) 15.24$°\mathrm{C}$          (b) 15.00°C

(c) 24.15$°\mathrm{C}$          (d) None of the above

There is formation of layer of snow x cm thick on water, when the temperature of air is $-\mathrm{\theta }°\mathrm{C}$ (less than freezing point). The thickness of layer increases from x to y in the time t, then the value of t is given by
(1) $\frac{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}-\mathrm{y}\right)\mathrm{\rho L}}{2\mathrm{k\theta }}$                

(2) $\frac{\left(\mathrm{x}-\mathrm{y}\right)\mathrm{\rho L}}{2\mathrm{k\theta }}$

(3) $\frac{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}-\mathrm{y}\right)\mathrm{\rho L}}{\mathrm{k\theta }}$                 

(4) $\frac{\left(\mathrm{x}-\mathrm{y}\right)\mathrm{\rho Lk}}{2\mathrm{\theta }}$

A composite metal bar of uniform section is made up of  equal lengths of copper,  nickel and  aluminium. Each part being in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at 100$°\mathrm{C}$ and the aluminium end at 0$°\mathrm{C}$. The whole rod is covered with belt so that there is 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 ?

(a) 23.33$°\mathrm{C}$ and 78.8$°\mathrm{C}$        (b) 88.89 $°\mathrm{C}$ and 22.22 $°\mathrm{C}$
(c) 50$°\mathrm{C}$ and 30$°\mathrm{C}$                (d) 30$°\mathrm{C}$ and 50$°\mathrm{C}$

Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle ABC, which is right-angled at B. The points A and B are maintained at temperatures T and $\sqrt{2}\mathrm{T}$ respectively. In the steady state, the temperature of point C is ${\mathrm{T}}_{\mathrm{C}}$. Assuming that only heat conduction takes place, $\frac{{\mathrm{T}}_{\mathrm{C}}}{\mathrm{T}}$ is equal to:
1. $\frac{1}{\left(\sqrt{2}+1\right)}$
2. $\frac{3}{\left(\sqrt{2}+1\right)}$
3. $\frac{1}{2\left(\sqrt{2}-1\right)}$                  
4. $\frac{1}{\sqrt{3}\left(\sqrt{2}-1\right)}$

The only possibility of heat flow in a thermos flask is through its cork which is 75 ${\mathrm{cm}}^2$ in area and 5 cm thick. Its thermal conductivity is 0.0075 cal/cmsec$°\mathrm{C}$. The outside temperature is 40$°\mathrm{C}$ and latent heat of ice is 80 cal ${\mathrm{g}}^{-1}$. Time taken by 500 g of ice at 0$°\mathrm{C}$ in the flask to melt into water at 0$°\mathrm{C}$ is -

(a) 2.47 hr
(b) 4.27 hr
(c) 7.42 hr
(d) 4.72 hr