A block of ice at $-20\,^oC$ having a mass of $2\, kg$ is added to a $3\, kg$ water at $15\,^oC$. Neglecting heat losses and the heat capacity of the container

$20\, gm$ of boiling water is poured into an ice-cold brass vessel (specific heat $0.1\, cal/gm-\,^oC$) of mass $100\, gm$. The resulting temperature is ........ $^oC$

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 ............ $^{\circ} C / s$

$80\, gm$ of water at $30°C$ are poured on a large block of ice at $0°C.$ The mass of ice that melts is ........ $gm$

sphere of $0.047 \;kg$ aluminium is placed for sufficient time in a vessel containing boiling water, so that the sphere is at $100\,^{\circ} C .$ It is then immediately transfered to $0.14 \;kg$ copper calorimeter containing $0.25\; kg$ water at $20\,^{\circ} C$. The temperature of water rises and attains a steady state at $23\,^{\circ} C$. Calculate the specific heat capacity of aluminium in $kJ\;kg^{-1} K^{-1}$ 

One end of a $2.35\,\,m$ long and $2.0\,\,cm$ radius aluminium rod$(K = 235 \,\,W.m^{-1}K^{-1})$ is held at $20^0\,\,C$. The other end of the rod is in contact with a block of ice at its melting point. The rate in $kg.s^{-1}$ at which ice melts is

[Take latent heat of fusion for ice as $\frac{{10}}{3} ×10^5 J.kg^{-1} $]