Question

A thermally insulated vessel contains some water at $0^{o}C$. The vessel is connected to a vacuum pump to pump out water vapor. This results in some water getting frozen. It is given latent heat of vaporization of water at $0^{o}C=21\times {10}^{5}J/kg$ and latent heat of freezing of water $=3.36\times {10}^{5}J/kg.$ The maximum percentage amount of water that will be solidified in this manner will be :

• A. $86.2\%$
• B. $33.6\%$
• C. $21\%$
• D. $24.36\%$

Answer 1

The correct option is A $86.2\%$

Let $x$% of water gets frozen.
Amount of heat lost during freezing is used to convert$(1-x)$% of water to steam.
$\therefore x\times 3.36\times {10}^5=(1-x)\times 21\times {10}^5$
$\therefore x=(1-x)\times 6.25$
$\therefore x=\frac{6.25}{7.25}=86.21$%