Thermal Properties of Matter

JEE Main level, single correct, medium

77 of 126

Question 77 of 126

A thermally insulated vessel contains 150g150g of water at 0∘C0^{\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∘C0^{\circ}C itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water =2.10×106Jkg−1=2.10\times {10}^{6}Jk{g}^{-1} and Latent heat of Fusion of water =3.36×105Jkg−1=3.36\times {10}^{5}Jk{g}^{-1} )

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Answer: (B) 20g20g

Suppose mm grams of water evaporate. Then, heat required
ΔQreq=mLv\Delta {Q}_{req}=m{L}_{v}
Mass that converts into ice =(150−m)=\left(150-m\right)
Heat released in the process,
ΔQrel=(150−m)Lf\Delta {Q}_{rel}=\left(150-m\right){L}_{f}
Now, ΔQrel=ΔQreq\Delta {Q}_{rel}=\Delta {Q}_{req}
(150−m)Lf=mLv\left(150-m\right){L}_{f}=m{L}_{v}
m(Lf+Lv)=150Lfm\left({L}_{f}+{L}_{v}\right)=150 {L}_{f}
m=150LfLf+Lvm=\dfrac{150{L}_{f}}{{L}_{f}+{L}_{v}}
m=20gm=20 g

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