The specific heat of a metal at low temperatures varies according to $S = aT^3$ where a is a constant and $T$ is the absolute temperature. The heat energy needed to raise unit mass of the metal from $T = 1 K$ to $T = 2 K$ is

Thermocouple is an arrange ment of two different metal to :-

$2\, kg$ of ice at $-20°C$ is mixed with $5\, kg$ of water at $20°C$ in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $1\, kcal/kg\, per °C$ and $0.5\, kcal/kg/°C$ while the latent heat of fusion of ice is $80\, k\,cal/kg$ ........ $kg$

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 $kJ\;kg^{-1} K^{-1}$ 

Find the quantity of heat required to convert $40\; gm$ of ice at $-20^{\circ} C$ into water at $20^{\circ} C$. Given $L _{\text {ice }}$ $=0.336 \times 10^6 J / kg$.

specific heat of ice $=2100 \;J / kg - K$ sp heat of water= $4200\; J / kg - K$

A beaker contains $200\, gm$ of water. The heat capacity of the beaker is equal to that of $20\, gm$ of water. The initial temperature of water in the beaker is $20°C.$ If $440\, gm$ of hot water at $92°C$ is poured in it, the final temperature (neglecting radiation loss) will be nearest to........ $^oC$