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

A sphere, a cube and a thin circular plate, all made of the same material and having the same mass are initially heated to a temperature of 1000°C. Which one of these will cool first ?
(1) Plate                     

(2) Sphere

(3) Cube                     

(4) None of these

Two identical conducting rods are first connected independently to two vessels, one containing water at 100$°\mathrm{C}$ and the other containing ice at 0$°\mathrm{C}$. In the second case, the rods are joined end to end and connected to the same vessels. Let ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ g / s be the rate of melting of ice in two cases respectively. The ratio of ${\mathrm{q}}_1$/${\mathrm{q}}_2$ is

(a) $\frac{1}{2}$                 (b) $\frac{2}{1}$
(c) $\frac{4}{1}$                 (d) $\frac{1}{4}$

A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature 120$°\mathrm{C}$, then -

(1) Both the cube and the sphere cool down at the same rate

(2) The cube cools down faster than the sphere

(3) The sphere cools down faster than the cube

(4) Whichever is having more mass will cool down faster

Two bodies \(A\) and \(B\) have thermal emissivities of \(0.01\) and \(0.81\) respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength \(\lambda_B\) corresponding to maximum spectral radiancy in the radiation from \(B\) is shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from \(A\), by \(1.00~\mu\text{m}\). If the temperature of \(A\) is \(5802~\text{K}\):