Question

To use the sun, a parametric mirror is used to focus 1 m^2 of sunlight onto a well-insulated container that contains 5 liters of water at room temperature (20°C) and 1 atm of pressure. The mirror provides 1368 W of power while the sun is shining, which it provides on average 4.6 hours per day in New Hampshire (during other times the sun is too high or too low to hit the mirror). Note that the specific heat of steam is 1865 . J/kg∙K

a.At the end of an average day, what is the temperature inside the container?

b. If the container were made of steel, as many pressure vessels are, would it be able to contain the heated water vapor?

Answer 1

5 liter water into kg =1000×5×10^(-3)= 5 kg

a.

Energy received by the water in a day = P * t = 1368×4.6×60×60 = 22654080 J

Energy required for water to reach 100 degree Celsius = mSΔt = 5×4182×(100 - 20)

= 1672800 J

Now Converting into steam so energy required

E = mL = 5×22.6×105 = 11300000 J

E_total = 1672800 + 11300000

= 12972800 J

So remaing energy = 22654080 - 12972800

= 9681280 J

This energy goes to increases to temperature of steam

E = mSΔt

Specific heat of steam = 1865 J/kgk

9681280 = 5×1865×(T - 100)

T = 1138.2 °C

b.

No, because heat losses due to Conduction.