Question

Some water at $0^{\circ} C$ is placed in a large insulated enclosure (vessel). The water vapour formed is pumped out continuously. What fraction of the water will ultimately freeze, if the latent heat vaporization is seven times the latent heat of fusion?

• A. $7 / 8$
• B. $8 / 7$
• C. $3 / 8$
• D. $5 / 8$

Answer 1

Answer: (A)

$m=$ mass of water, $f=$ fraction which freezes
$L _{1}=$ latent heat of vaporization
$L _{2}=$ latent heat of fusion
$\therefore L _{1}=7 L _{2}$
Mass of water frozen $= mf$
Heat lost by freezing water $= m fL _{2}$
Mass of vapour formed $= m (1- f )$
Heat gained by vapour $= m (1- f ) L _{1}$
$mfL _{2}= m (1- f ) \times 7 L _{2}$
$f=7-7 f$ or $f=7 / 8$