9. (a) The energy that leaves the aluminum as heat has magnitudeQ=maca(Tai−Tf), wheremaisthe mass of the aluminum,cais the speciFc heat of aluminum,Taiis the initial temperature of thealuminum, andTfis the Fnal temperature of the aluminum-water system. The energy that entersthe water as heat has magnitudeQ=mwcw(Tf−Twi), wheremwis the mass of the water,cwisthe speciFc heat of water, andTwiis the initial temperature of the water. The two energies are thesame in magnitude since no energy is lost. Thus,maca(Tai−Tf)=mwcw(Tf−Twi⇒Tf=macaTai+mwcwTwimaca+mwcw.The speciFc heat of aluminum is 900 J/kg·K and the speciFc heat of water is 4190 J/kg·K. Thus,Tf=(0.200 kg)(900 J/kg·K)(100◦C) + (0.0500 kg)(4190 J/kg·K)(20◦C)(0.200 kg)(900 J/kg·K) + (0.0500 kg)(4190 J/kg·
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.