If you start with 172 g of water at 29
◦
C, how
much heat must you add to convert all the
liquid into vapor at 100
C? Assume no heat
is lost to the surroundings.
Answer in units of kJ
First heat liquid H2O (Cp = 4.18 J/g K) from 29oC to 100oC...
dH = mCpdT
dH = 172 g * 4.18 J/g K * (100oC - 28oC) = 51765 J = 51.8 kJ
Then evaporate the water @100 oC...
dH evap (@100 oC) = 2676 J/g from the steam tables
172 g * 2676 J/g = 460,272 J = 460.3 kJ
So the total heat added is the sum of the sensible heat change (heating the liquid) and the latent heat change (evaporation)
51.8 kJ + 460.3 kJ = 512.1 kJ
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Verified answer
First heat liquid H2O (Cp = 4.18 J/g K) from 29oC to 100oC...
dH = mCpdT
dH = 172 g * 4.18 J/g K * (100oC - 28oC) = 51765 J = 51.8 kJ
Then evaporate the water @100 oC...
dH evap (@100 oC) = 2676 J/g from the steam tables
172 g * 2676 J/g = 460,272 J = 460.3 kJ
So the total heat added is the sum of the sensible heat change (heating the liquid) and the latent heat change (evaporation)
51.8 kJ + 460.3 kJ = 512.1 kJ