The Ice Sphere Melting Chamber · AI Generator #GEN-F91F0685

Physics · thermodynamics

Problem

A spherical chamber of radius R=0.50  mR = 0.50\;\text{m} contains water vapor at temperature T0=400  KT_0 = 400\;\text{K} and pressure P0=2.0×105  PaP_0 = 2.0 \times 10^5\;\text{Pa}. A solid ice sphere of radius r=0.10  mr = 0.10\;\text{m} at 0°C0°\text{C} is suddenly introduced into the chamber. The chamber walls are perfectly insulating, and the ice melts completely while the water vapor condenses partially. After thermal equilibrium is reached, all the water is in liquid form at Tf=100°CT_f = 100°\text{C}. Find the initial mass of water vapor in the chamber. Use: latent heat of fusion Lf=3.34×105  J/kgL_f = 3.34 \times 10^5\;\text{J/kg}, latent heat of vaporization Lv=2.26×106  J/kgL_v = 2.26 \times 10^6\;\text{J/kg}, specific heat of water cw=4186  J/(kg⋅K)c_w = 4186\;\text{J/(kg·K)}, and assume water vapor behaves as an ideal gas with molar mass M=18.0  g/molM = 18.0\;\text{g/mol}.

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