Question

A thermally insulated vessel contains $150g$ of water at $0^{\circ }C$. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at $0^{\circ }C$ itself. The mass of evaporated water will be closest to
(Latent heat of vaporization of water $=2.10\times {10}^{6}Jk{g}^{-1}$ and Latent heat of fusion of water $=3.36\times {10}^{5}Jk{g}^{-1})$

• A. $130g$
• B. $35g$
• C. $20g$
• D. $150g$

Answer 1

The correct option is C $20g$

Suppose $m$ grams of water evaporate. Then, heat required
$△Q_{req}=m{L}_v$
Mass that converts into ice $=(150-m)$
Heat released in this process
$△Q_{rel}=(150-m)L_f$
Now,
$△Q_{rel}=△Q_{req}$
$(150-m)L_f=m{L}_V$
$m(L_f+L_v)=150L_f$
$m=\frac{150L_f}{L_f+L_v}$
$m=20g$