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62. A sealed room has a volume of 24 m3. Its filled with air, which may be assumed to be diatomic, at a temperature of 24 °C and a pressure of 9.83 x 104 Pa, A 1.00-k block of ice at its melting point is placed in the room. Assume the walls of the room transfer no heat. What is the equilibrium temperature?
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Answer #1

Consider equilibrium temperature as T

Ideal gas equation, PV = nRT
T = 273+24 = 297 K
n = PV/RT = 98300*24/8.314*297 = 955.428

Balancing heat
mass of ice block = m = 1 kg
specific heat of water = 4186 J/kg-K
latent heat of ice = 334000 J/kg

nCv (delta T) = m(334000) + m(4186) (T-0)

PV/RT * (5/2) R * (24-T) = 334000 + 4186T
955.428*2.5*8.314(24-T) = 334000 + 4186T
476606 - 19858.58T = 334000 + 4186T
T = 5.93 degree Celsius

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