A piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of $h$ is

[Latent heat of ice is $3.4 \times 10^{5}\; J / k g$ and $g=10\; N / kg ]$

In an experiment a sphere of aluminium of mass $0.20\, kg$ is heated upto $150\,^oC$. Immediately, it is put into water of volume $150\, cc$ at $27\,^oC$ kept in a calorimeter of water equivalent to $0.025\, kg$. Final temperature of the system is $40\,^oC$. The specific heat of aluminium is ............ $J/kg\,-\,^oC$ (take $4.2\, Joule= 1\, calorie$)

A $2\,kg$ copper block is heated to $500^o\,C$ and then it is placed on a large block of ice  at $0^o\,C$. If the specific heat capacity of copper is $400\, J/kg/ ^o\,C$ and latent heat of  fusion of water is $3.5 \times 10^5\, J/kg$, the amount of ice, that can melt is :-

Which of the following material is used to make calorimeter?

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box contains one mole of helium at temperature $(7/3)$ $T_0$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases,$T_f$  in terms of $T_0$ is

Heat is being supplied at a constant rate to the sphere of ice which is melting at the rate of $0.1 \,gm / s$. It melts completely in $100 \,s$. The rate of rise of temperature thereafter will be ............ $^{\circ} C / s$