A large room contains a volume of air of Va = 11 m3 at a temperature of Ta = 55° F. It also contains a bathtub holding a volume of water of Vw = 0.51 m3 at a temperature of Tw = 111° F. Part (a) If the density of the air at Ta is ρa = 1.25 kg/m3, calculate the mass of air in the room in kilograms. Part (b) If the density of the water at Tw is ρw = 1000 kg/m3, calculate the mass of the water in the bathtub in kilograms. Part (c) Take the room and water as an isolated system. Write an equation for the equilibrium temperature of the system T in terms of ma, Ta, mw, Tw, and the specific heat capacity of the air ca and the water cw.
Problem 3: A large room contains a volume of air of Va = 11 m3 at a temperature of Ta = 55° F. It also contains a bathtub holding a volume of water of Vw = 0.51 m3 at a temperature of Tw = 111° F.
Part (a) If the density of the air at Ta is ρa = 1.25 kg/m3, calculate the mass of air in the room in kilograms.
Part (b) If the density of the water at Tw is ρw = 1000 kg/m3, calculate the mass of the water in the bathtub in kilograms.
Part (c) Take the room and water as an isolated system. Write an equation for the equilibrium temperature of the system T in terms of ma, Ta, mw, Tw, and the specific heat capacity of the air ca and the water cw.
Part (d) Calculate the final temperature of the system in kelvin, assuming a constant specific heat for the water of cw = 4180 J/kg⋅K and a constant specific heat capacity for the air of ca = 1010 J/kg⋅K.
Part (e) Calculate the change in the internal energy ΔU of the room-water system in joules.
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