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Question:

A thermally insulated vessel contains 150g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water = 2.10 × 10⁶ J kg⁻¹ and Latent heat of Fusion of water = 3.36 × 10⁵ J kg⁻¹)

35 g

130 g

20 g

150 g

Solution:

Correct option is C. 20 g
Suppose 'm' gram of water evaporates then, heat required ΔQreq = mLv
Mass that converts into ice = (150 - m)
So, heat released in this process ΔQrel = (150 - m)Lf
Now, ΔQrel = ΔQreq
(150 - m)Lf = mLv
m(Lf + Lv) = 150Lf
m = 150Lf / (Lf + Lv)
m ≈ 20 g