You need three steps to get liquid water at 0 °C to vapor at 167 °C:
1. Heat it from 0 °C to 100 °C
2. Turn the liquid water to vapor, all at 100 °C
3. Heat the vapor from 100 °C to 167 °C
I split the entire heating process up because there are different heat capacities involved.
1. The specific heat capacity of water* is around 4.2 J/(g K).
So energy to heat the specified amount of water from 0 °C to 100 °C amounts to:
Q₁ = 4.2 J/(g K) × 457 g × 100 K ≈ 192 kJ
2. The heat of evaporation of is** 2,257 J/g
Q₂ = 2,257 J/g × 457 g ≈ 1,031 kJ
3. The specific heat capacity of vapor* is around 2.1 J/(g K)
Q₃ = 2.1 J/(g K) × 457 g × 67 K ≈ 64 kJ
For the entire process we simply add Q₁, Q₂, and Q₃:
Q = 192 kJ + 1031 kJ + 64 kJ = 1,287 kJ
This figure is rounded, you can get better precision if you take more precise values for the specific heat capacities if necessary.
Hope that helped.
* I use the figure from this table: https://en.wikipedia.org/wiki/Heat_capacity#Table_...
** I use the figure from this paragraph: https://en.wikipedia.org/wiki/Water#Polarity_and_h...
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Answers & Comments
You need three steps to get liquid water at 0 °C to vapor at 167 °C:
1. Heat it from 0 °C to 100 °C
2. Turn the liquid water to vapor, all at 100 °C
3. Heat the vapor from 100 °C to 167 °C
I split the entire heating process up because there are different heat capacities involved.
1. The specific heat capacity of water* is around 4.2 J/(g K).
So energy to heat the specified amount of water from 0 °C to 100 °C amounts to:
Q₁ = 4.2 J/(g K) × 457 g × 100 K ≈ 192 kJ
2. The heat of evaporation of is** 2,257 J/g
Q₂ = 2,257 J/g × 457 g ≈ 1,031 kJ
3. The specific heat capacity of vapor* is around 2.1 J/(g K)
Q₃ = 2.1 J/(g K) × 457 g × 67 K ≈ 64 kJ
For the entire process we simply add Q₁, Q₂, and Q₃:
Q = 192 kJ + 1031 kJ + 64 kJ = 1,287 kJ
This figure is rounded, you can get better precision if you take more precise values for the specific heat capacities if necessary.
Hope that helped.
* I use the figure from this table: https://en.wikipedia.org/wiki/Heat_capacity#Table_...
** I use the figure from this paragraph: https://en.wikipedia.org/wiki/Water#Polarity_and_h...