Question

Steam at $100{}^\circ C$ is passed into $20g$ of water acquires a temperature of $80{}^\circ C$, the mass of water presents will be [Take specific heat of water $1ca{{\lg }^{-1}}{{c}^{-1}}$ and also latent heat of steam is $540{{g}^{-1}}$
$\begin{align}
  & A.31.5g \\
 & B.42.5g \\
 & C.22.5g \\
 & D.24g \\
\end{align}$

Answer 1

- Hint: First find the heat required to convert $100{}^\circ C$ water to $100{}^\circ C$ vapour. Then calculate the total heat required for the process and from that. After this calculate the mass of water present at this occasion.

Formula used:
$H=mST$
Where $m$ is the mass of water, $S$ is the specific heat of water and $T$ is the temperature increase taking place.
\[H=mL\]
Where $L$ be the latent heat of steam.$L$

Complete step-by-step solution
As per the question, it is mentioned that, the water acquires a temperature up to $80{}^\circ C$ when
Steam at $100{}^\circ C$ is passed through it. The mass of water present at this time is $20g$ .
Therefore firstly let us calculate the heat energy required to increase the temperature in to $100{}^\circ C$ will be,
$H=mST$
Where $m$ is the mass of water, $S$ is the specific heat of water and $T$ is the temperature increase taking place.
As per the equation,
$S=1ca{{\lg }^{-1}}{{c}^{-1}}$
$T=100-80=20{}^\circ C$
Substitute these all in the equation of heat will give,
\[H=20\times 1\times 20=400cal\]
Now the temperature of water has reached $100{}^\circ C$ , it is still in a liquid state.
Now let us convert the liquid state in to vapour state,
Therefore we can write that,
The heat consumption during the process will be,
\[H=mL\]
In the question it is mentioned that the latent heat of steam is,
\[L=540{{g}^{-1}}\]
Substituting the value in it will results in,
\[H=20\times 540=10800cal\]
Therefore the total heat produced or developed will be
\[L=10800cal+400cal=11200cal\]
From this we can calculate the mass of the water.
\[\begin{align}
  & m=\dfrac{11200}{400}g \\
 & m=22.5g \\
\end{align}\]
Therefore the mass of water will be \[22.5g\] .
Hence the correct answer is given as option C.

Note: Two general forms of latent heat will be latent heat of fusion in the case of melting and latent heat of vaporization in the case of boiling. These names explain the direction of energy flow if varying from one phase to the next. That means from solid to liquid, and liquid to gas.