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. Parts (a), (b), (c) are already complete. Just need parts (d) and (e). 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. ma = 13.75 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. mw = 510 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. T = ( mw cw Tw + ma ca Ta )/( mw cw + ma ca ) 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.

Problem 3:  A large room contains a volume of air of V_a = 11 m³ at a temperature of T_a = 55° F. It also contains a bathtub holding a volume of water of V_w = 0.51 m³ at a temperature of T_w = 111° F. 

Parts (a), (b), (c) are already complete. Just need parts (d) and (e).

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. 

m_a = 13.75

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. 

m_w = 510 

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. 

T = ( m_w c_w T_w + m_a c_a T_a )/( m_w c_w + m_a c_a ) 

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.