Thermal Propert...

The volume of an air bubble is doubled as it rises from the bottom of a lake to its surface. If the atmosphere pressure is $$Hm$$ of mercury and the density of mercury is $$n$$ times that of lake water the depth of lake is :

What is the final temperature of the system ?

If, after some of the tea has been transferred to the thermos (as described in the passage), the teapot with its contents (at a temperature of $$80^{o}C$$) was placed or the insulated warmer for $$5$$ minutes, what would be the temperature at the end of this $$5$$ minutes period (Assume that no significant heat transfer occurs with the surrounding):

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

Three rods of identical cross-sectional area and made from the same metal from the sides of an isosceles triangle $$ABC$$ right angled at $$B$$. The points $$A$$ and $$B$$ are maintained at temperatures $$T$$ and $$\sqrt 2 T$$ respectively in the steady state. Assuming that only heat conduction takes place temperature of point $$C$$ will be:

A solid aluminium sphere and a solid lead sphere of the same radius are heated to the same temperature and allowed to cool under identical surrounding temperatures. The specific heat capacity of aluminium = $$
900\space J/kg^{0}C$$ and that of the lead = $$ 130 \space J/kg^{0}C$$. The density of lead = $$10^{4} \space kg/m^{3}$$ and that of aluminum = $$ 2.7 \times 10^{3} \space kg/m^{3}
\space kg/m^{3}$$. Assume that the emissivity of both the
spheres is the same

    The ration of the rate of fall of temperature of the aluminium sphere to the rate of fall of temperature of the lead sphere is 

Two identical calorimeters, each of water equivalent 100 g and volume 200 cm$$^3$$, are filled with water and a liquid. They are placed in identical constant-temperature enclosures to cool down. The temperatures are plotted at different times (the choice of units are completely arbitrary) as shown in the figure. If the density of the liquid is 800 kgm$$^{-3}$$, then its specific heat capacity is

Assume that the thermal conductivity of copper is twice that of aluminium and four times that of brass. Three metal rods made of copper, aluminium and brass are each 15 cm long and 2 cm in diameter. These rods are placed end to end, with aluminium between the other two. The free ends of the copper and brass rods are maintained at $$100^{0}C$$ and $$0^{0}C$$, respectively. The system is allowed to reach the steady-state condition. Assume there is no loss of heat anywhere.
  When a steady-state condition is reached everywhere, which of the following statements is true?

A solid aluminium sphere and a solid lead sphere of the same radius are heated to the same temperature and allowed to cool under identical surrounding temperatures. The specific heat capacity of aluminium = $$
900\space J/kg^{0}C$$ and that of the lead = $$ 130 \space J/kg^{0}C$$. The density of lead = $$10^{4} \space kg/m^{3}$$ and that of aluminum = $$ 2.7 \times 10^{3} \space kg/m^{3}\space kg/m^{3}$$. Assume that the emissivity of both the
spheres is the same

   When the temperature of spheres T is not too different from the surrounding temperature, the radiating object obeys

 An immersion heater, in an insulated vessel of negligible heat capacity, brings 100 g of water to the boiling point from $$16^{0}C$$ in 7 min. Then
         Power of heater is nearly