Question

A large punch bowl holds 3.95 kg of lemonade (which is essentially water) at 20.0

Answer 1

Apply First Law of Thermodynamics :
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Q = [ Delta U sub I ] + [ Delta U sub W ] + W sub B

Q ~ 0.0 & W sub B = 0.0

[ Delta U sub I ] = [ mI ] [ CPI ( 0.0 - (-10.2) ) + HSF + CPW ( TE - 0.0 ) ]

[ Delta U sub I ] = [0.370 ] [( 1.96 ) ( (10.2 ) + 335 + ( 4.187 ) ( TE ) ]

[ Delta U sub I ] = [ 7.397 + 123.95 + ( 1.549 ) ( TE ) ]

[ Delta U sub I ] = 131.347 + ( 1.549 ) ( TE )

[ Delta U sub W ] = [msubW] [ CPW ( TE -20.0 )]

[ Delta U sub W ] = [ 4.05 ] [ (4.187)( TE ) - 83.74 ]

[ Delta U sub W ] = (16.95735 )( TE ) - 339.147

0.0 = [ 131.347 + 1.549 ( TE ) ] + [ (16.95735 )( TE ) - 339.147 ]

(18.51) ( TE ) = 207.8

TE = 11.23 deg C <-------------------------------

m sub I remaining = 0.0 kg <---------------------------------