A copper block of mass $5.0\, kg$ is heated to a temperature of $500^{\circ} C$ and is placed on a large ice block. What is the maximum amount of ice (ઇન $kg$) that can melt? [Specific heat of copper: $0.39\, Jg ^{-1 \circ} C ^{-1}$ and latent heat of fusion of water : $335 \,J g ^{-1}$ ]

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 $4.2\, Joule= 1\, calorie$)

Ice in a freezer is at $-7^{\circ} C .100 \,g$ of this ice is mixed with $200 \,g$ of water at $15^{\circ} C$. Take the freezing temperature of water to be $0^{\circ} C$, the specific heat of ice equal to $2.2 \,J / g { }^{\circ} C$, specific heat of water equal to $4.2 \,J / g ^{\circ} C$ and the latent heat of ice equal to $335 \,J / g$. Assuming no loss of heat to the environment, the mass of ice in the final mixture is closest to .......... $g$

A mass of material exists in its solid format its melting temperature $0\,^o  C$. The following processes then occur to the material

Process $-1$:An amount of thermal energy $Q$ is added to the material and $\frac{2}{3}$ of the material melts.

Process $-2$:An identical additional amountof thermal energy $Q$ is added to the materlal is now a liquid at $4\,^o C$

........ $^oC$ is the ratio of the latent heat of fusion to the specific heat of the liquid for this material.

If an electric heater is rated at $1000\, W$, then the time required to heat one litre of water from $20\,^oC$ to $60\,^oC$ is

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