A thermally insulated vessel contains some water at 0^0C . vessel is connected to a vacuum pump to p

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10-1.Thermometry, Thermal Expansion and Calorimetry

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

A

$86.2$

B

$33.6 $

C

$21$

D

$24.36$

Solution

Let $m_{1}$ be the amount of water that freezes and $m_{2}$ be the amount of water that vaporizes.

Therefore, heat is taken from frozen water $=$ Heat given to water vapors.

$\Longrightarrow m_{1}\left(3.36 \times 10^{5}\right)=m_{2}\left(21 \times 10^{5}\right)$

$\Longrightarrow m_{2}=0.16 m_{1}$

Percentage of water solidified $=\frac{m_{1}}{m_{1}+m_{2}} \times 100 \%$

$=86.2 \%$

Standard 11

Physics

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(AIPMT-1988)