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If all this energy is added to 50 kg of water (the amount of water in a 165-lb person) at 37°C, what is the final state of the water?

- The specific heat of water is 4180 J/kg⋅°C.
- The heat of vaporization at the boiling temperature for water is [tex]2.256 \times 10^6 \text{ J/kg}[/tex].
- The specific heat of steam is 1970 J/kg⋅°C.

Answer :

Answer:

Vapors

Explanation:

We take into account that all the energy from the lightning has been transformed into steam.

[tex]\Delta U = Q - W\\Q = mC \Delta T\\Q = mL[/tex]

We calculate the amount of energy required by water to convert into steam.

[tex]Q_{water} = 50 \times \times 4180 \times (100-37)\\= 1.132 \times 10^7 \ J[/tex]

[tex]Q_{change\ to\ steam} = 50 \times 2.256 \times 106 \\= 1.128 \times 10^8 \ J[/tex]

[tex]Q_{total} = 1.132 \times 10^7 + 1.128 \times 10^8\\= 1.126 \times 10^8 \ J[/tex]

From the lightning we received [tex]10^{10} \ J[/tex] of energy, out of which [tex]1.126 \times 10^8[/tex] has been used to convert the water into steam.

Energy left = [tex]10^{10} - 1.126 \times 10^8 = 9.88 \times 10^9 \ J[/tex]

We use this energy to convert steam into vapors.

[tex]Q = \Delta E[/tex]

[tex]Q = \Delta E = mc (T_{f} - T{i})\\T_{f} = \frac {\Delta E}{mc} + T_{i}\\ \\T_{f} = 100 + \frac{9.88 \times 10^{10}}{50 \times 1970}\\T_{f} = 100 + 10^8\\T_{f} = 10 ^{ \ 8} \ {^ \circ } C[/tex]

With this temperature, we can easily interpret that the vapors will be dissociated in hydrogen and oxygen particles.

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Rewritten by : Barada