Get Delta U to heat water from 25 C to 100 C and Delta U to vaporize the water at 100 C.
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Delta U1 = ( m ) ( Cv ) ( T100 - T25 )
Delta U1 = ( 100 g ) ( 4.18 J / g - C ) ( 100 C - 25 C ) = 31350 J
Delta U2 = ( m ) ( u sub fg at 100C )
Delta U2 = ( 100 g ) ( 2257 J/g ) = 225700 J
Q = Delta U1 + Delta U2
Q = 31350 J + 225700 J = 257050 J = 257.05 kJ <----------------
Supposing you mean bringing the water to 100°C, instead of bringing to 100°C and boiling it all away:
(4.18 J/g·°C) x (100 g) x (100 - 25)°C = 31350 J = 3.14 kJ
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Get Delta U to heat water from 25 C to 100 C and Delta U to vaporize the water at 100 C.
------------------------------------------------------------------------------------------------------------------------
Delta U1 = ( m ) ( Cv ) ( T100 - T25 )
Delta U1 = ( 100 g ) ( 4.18 J / g - C ) ( 100 C - 25 C ) = 31350 J
Delta U2 = ( m ) ( u sub fg at 100C )
Delta U2 = ( 100 g ) ( 2257 J/g ) = 225700 J
Q = Delta U1 + Delta U2
Q = 31350 J + 225700 J = 257050 J = 257.05 kJ <----------------
Supposing you mean bringing the water to 100°C, instead of bringing to 100°C and boiling it all away:
(4.18 J/g·°C) x (100 g) x (100 - 25)°C = 31350 J = 3.14 kJ