$A$ small quantity,mass $m$,of water at a temperature $\theta$ (in $^oC$) is poured onto a large mass $M$ of ice which is at its melting point. If $c$ is the specific heat of water and $L$ is the latent heat of fusion of ice,then the mass of ice melted is given by

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

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

$A$ block of ice of mass $120\,g$ at temperature $0^{\circ}C$ is put in $300\,g$ of water at $25^{\circ}C$. The $x\,g$ of ice melts as the temperature of the water reaches $0^{\circ}C$. The value of $x$ is.
[Use: Specific heat capacity of water $= 4200\,J\,kg^{-1}K^{-1}$,Latent heat of ice $= 3.5 \times 10^{5}\,J\,kg^{-1}$]

$A$ tap supplies water at $10\,^{\circ}C$ and another tap at $100\,^{\circ}C$. How many $kg$ of hot water must be taken so that we get $20\, kg$ of water at $35\,^{\circ}C$?

In an experiment on the specific heat of a metal,a $0.20 \; kg$ block of the metal at $150 \; ^{\circ}C$ is dropped in a copper calorimeter (of water equivalent $0.025 \; kg$) containing $150 \; cm^{3}$ of water at $27 \; ^{\circ}C$. The final temperature is $40 \; ^{\circ}C$. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible,is your answer greater or smaller than the actual value for the specific heat of the metal?