The water equivalent of $20 \,g$ of aluminium (specific heat $0.2 \,cal \,g^{-1} {}^{\circ}C^{-1}$) is ......... $g$.

$A$ massless spring $(k = 800\, N/m)$,attached with a mass $(500\, g)$ is completely immersed in $1\, kg$ of water. The spring is stretched by $2\, cm$ and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass $= 400\, J/kg\, K$,specific heat of water $= 4184\, J/kg\, K$)

Equal masses of three liquids $A, B$ and $C$ have temperatures $10\,^{\circ}C$,$25\,^{\circ}C$ and $40\,^{\circ}C$ respectively. If $A$ and $B$ are mixed,the mixture has a temperature of $15\,^{\circ}C$. If $B$ and $C$ are mixed,the mixture has a temperature of $30\,^{\circ}C$. If $A$ and $C$ are mixed,the mixture will have a temperature of ........ $^{\circ}C$

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of $100^{\circ} C$,while the other one is kept at $0^{\circ} C$. If the two are brought into contact,then assuming no heat loss to the environment,the final temperature that they will reach is

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

$A$ thermos flask contains $250 \ g$ of coffee at $90^{\circ} C$. To this $20 \ g$ of milk at $5^{\circ} C$ is added. After equilibrium is established,the temperature of the liquid is (Assume no heat loss to the thermos bottle. Take specific heat of coffee and milk as $1.00 \ cal/g^{\circ} C$) (in $^{\circ} C$)