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

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 
(a) ${\mathrm{K}}_1+{\mathrm{K}}_2$           (b) $\frac{{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1+{\mathrm{K}}_2}$
(c) $\frac{{\mathrm{K}}_1+3{\mathrm{K}}_2}{4}$        (d) $\frac{3{\mathrm{K}}_1+{\mathrm{K}}_2}{4}$

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 

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

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

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 ?

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:

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 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 ?

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 -

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 ${\mathrm{\lambda }}_{\mathrm{B}}$ 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 $\mathrm{\mu m}$ . If the temperature of A is 5802 K -

A black body is at a temperature of 2880 K. The energy of radiation emitted by this object with wavelength between 499 nm and 500 nm is ${\mathrm{U}}_1$, between 999 nm and 1000nm is ${\mathrm{U}}_2$ and between 1499 nm and 1500 nm is ${\mathrm{U}}_3$. [Given : Wein's constant $\mathrm{b}=2.88\times {10}^6 \mathrm{nm} \mathrm{K}$}.  Then

Three rods of same dimensions are arranged as shown in figure they have thermal conductivities ${\mathrm{K}}_1, {\mathrm{K}}_2$ and ${\mathrm{K}}_3$ The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ and PQ then which of the following option is correct ?

Two metallic spheres ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are made of the same material and have identical surface finish. The mass of ${\mathrm{S}}_1$ is three times that of ${\mathrm{S}}_2$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of ${\mathrm{S}}_1$ to that of ${\mathrm{S}}_2$ is 

Three discs A, B and C having radii 2m, 4m, and 6m respectively are coated with carbon black on their surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm, respectively. The power radiated by them are ${\mathrm{Q}}_{\mathrm{a}}$, ${\mathrm{Q}}_{\mathrm{b}}$, and ${\mathrm{Q}}_{\mathrm{c}}$ respectively

A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is same , then

A solid copper cube of edges 1 cm is suspended in an evacuated enclosure. Its temperature is found to fall from 100$°\mathrm{C}$ to 99$°\mathrm{C}$ in 100 s . Another solid copper cube of edges 2 cm, with similar surface nature, is suspended in a similar manner. The time required for this cube to cool from 100$°\mathrm{C}$ to 99$°\mathrm{C}$ will be approximately -
(a) 25 s                  (b) 50 s  
(c) 200 s                 (d) 400 s

A body initially at 80$°\mathrm{C}$ cools to 64$°\mathrm{C}$ in 5 minutes and to 52$°\mathrm{C}$ in 10 minutes. The temperature of the body after 15 minutes will be 
(a) 42.7$°\mathrm{C}$                  (b) 35 $°\mathrm{C}$
(c) 47 $°\mathrm{C}$                    (d) 40 $°\mathrm{C}$

Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is 100$°\mathrm{C}$, then the temperature difference between the ends of other diagonal will be -

A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of 0.1 gm of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is $\frac{1}{4}$ that of first, the rate at which ice melts in gm/sec will be -

One end of a copper rod of length 1.0 m and area of cross-section ${10}^{-3} {\mathrm{m}}^2$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is 92 cal/m-s $°\mathrm{C}$ and the latent heat of ice is $8\times {10}^4$ cal/kg, then the amount of ice which will melt in one minute is -
(a) $9.2\times {10}^{-3}$ kg         (b) $8\times {10}^{-3}$
(c) $6.9\times {10}^{-3}$              (d) $5.4\times {10}^{-3}$

An ice box used for keeping eatable cold has a total wall area of 1 ${\mathrm{metre}}^2$ and a wall thickness of 5.0 cm. The thermal conductivity of the ice box is K = 0.01 joule/metre-s-$°\mathrm{C}$. It is filled with ice at 0$°\mathrm{C}$ along with eatables on a day when the temperature is 30°C. The latent heat of fusion of ice is $334 \times {10}^3 joules/kg$. The amount of ice melted in one day is ( 1 day = 86,400 seconds ) 
(a) 776 gms            (b) 7760 gms  
(c) 11520 gms         (d) 1552 gms

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

A hot metallic sphere of radius r radiates heat. It's rate of cooling is

A solid copper sphere (density $\mathrm{\rho }$ and specific heat capacity c) of radius r at an initial temperature 200K is suspended inside a chamber whose walls are at almost 0K. The time required (in $\mathrm{\mu }$s) for the temperature of the sphere to drop to 100 K is 

One end of a copper rod of uniform cross-section and of length 3.1 m is kept in contact with ice, and the other end with water at 100°C. At what point along its length should a temperature of 200°C be maintained so that in steady-state, the mass of ice melting be equal to that of the steam produced in the same interval time?
(Assume that the whole system is insulated from the surroundings. Latent heat of fusion of ice and vaporisation of water are 80 cal/gm and 540 cal/gm respectively)
     

A sphere and a cube of same material and same volume are heated upto same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiations emitted will be

An object kept in a large room having an air temperature of 25° C takes 12 minutes to cool from 80° C to 70° C. The time taken to cool for the same object from 70° C to 60° C would be nearly -

Gas thermometers are more sensitive than liquid thermometers because: