I have tried part c and my algebra is leading me astray. A large room contains a
ID: 1470455 • Letter: I
Question
I have tried part c and my algebra is leading me astray.
A large room contains a volume of air of Va = 13 m^3 at a temperature of Ta = 51 degree degreeF. It also contains a bathtub holding a volume of water of Vw = 054 m3 at a temperature of Tw = 108 degree degreeF. Randomized Variables Va = 13 m3^3 Ta = 51 degree F Vw = 054 m^3 Tw = 108degree If the density of the air at Ta is ga = 1.25 kg/m3, calculate the mass of air in the room in kilograms. 0 ^20% If the density of the water at Tw is gw = 1000 kg/m3, calculate the mass of the water in the bathtub in kilograms. 20% Take the room and water as an isolated system. Write an equation for the equilibrium temperature of the system Tin terms of ma, Ta, mw, Tw, and the specific heat capacity of the air ca and the water cw. 20% calculate the final temperature of the system in kclvin, 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. O A 20% Calculate the change in the internal energy AU of the room-water system in joules.Explanation / Answer
we use the enrgy conservation principle.
heat lost by water = heat gained by air
mw*cw(108-T) =ma*ca(T-51)
108mwcw-mwcwT =ma*caT -51ma*ca
108mwcw+51ma*ca=ma*caT+mwcwT
T=(108mwcw+51ma*ca)/(ma*ca+mwcw)