Question

The ratio of the latent heat of steam to latent heat of ice
\eqalign{ & A.\dfrac{4}{9} \cr & B.\dfrac{9}{4} \cr & C.\dfrac{4}{{27}} \cr & D.\dfrac{{27}}{4} \cr & \cr}

Answer 1

When heat is given to ice it converts into water and ideally when the same amount of heat is taken from water we can convert it back to ice. Latent heat of ice deals with this particular property and during this process temperature doesn’t change or we can call it an isothermal process. Same with latent heat of steam i.e the amount of heat required to convert water into steam is called latent heat of steam.

Complete answer:
It's a natural process that if one substance is heated then obviously its temperature raises. For example consider water heated on a gas stove, its temperature rises after some time due to heat. But incase of phase change from ice to water it doesn’t happen. The amount of energy taken will be used to break attractive bonds between molecules of ice instead of increasing its kinetic energy i.e during phase change kinetic energy remains constant while potential energy changes.
Now, coming to latent heat of ice, It is the amount of heat taken in converting ice to water or the amount of heat given out when water is converted into ice.
In case of boiling water once water reaches 100 degree Celsius and if we continue heating water will go through phase change to steam at that temperature(at 1 bar pressure). This heat consumed for phase change is called latent heat of steam
Value of latent heat of ice is $80\dfrac{{calories}}{{gram}}$
Value of latent heat of steam is $540\dfrac{{calories}}{{gram}}$

Now ratio of latent heat of steam to ice would be $\dfrac{{540\dfrac{{calories}}{{gram}}}}{{80\dfrac{{calories}}{{gram}}}} = \dfrac{{54}}{8} = \dfrac{{27}}{4}$

So the answer would be option D.

Note:
In case of calorimetry problems one usually confuses between latent heat and specific heat. Latent heat is the amount of heat taken which inturn causes phase change where temperature remains constant. But in case of specific heat phase remains constant while temperature changes.